# import the library numpy as np
import numpy as np
# import the library matplotlib.pyplt as plt
import matplotlib.pyplot as plt
# set a seed for your calculations so that they are reproducible
x = np.random.seed (123456)
# generate 50 random integers from 1 to 50 using random.randint() and make a
# frequency histogram
x = np.random.randint (low = 1, high = 50, size = 50)
print (x)
plt.hist(x, bins = 5)
plt.show()
[ 2 43 44 48 44 28 33 24 37 9 11 11 13 12 21 44 48 23 39 35 15 7 43 3
48 5 31 46 24 21 21 46 6 24 37 12 36 30 40 17 35 19 16 48 33 28 21 18
11 47]
# generate 10000 random integers from 1 to 50 using random.randint() and make a
# frequency histogram
# compare with previous histogram
x = np.random.randint (low = 1, high = 50, size = 10000)
print (x)
plt.hist(x, bins = 5)
plt.show()
[29 21 15 ... 26 43 10]
# generate 1000 floating point numbers uniformly distributed from 1 to 100 and make a
# frequency histogram
x = np.random.uniform (low = 1, high = 100, size = 1000)
print (x)
plt.hist(x, bins = 5)
plt.show()
[15.40720343 33.3019995 60.85357536 70.17893769 83.89529375 51.52846284
89.32789053 76.0766353 8.06229506 67.01835898 69.47856097 6.71610033
80.27682751 12.87798528 97.91087392 64.46475082 12.3833652 1.57240569
48.07790592 77.0109991 20.75092395 12.59672253 93.43851365 77.92890378
70.8269827 52.28232241 48.17939703 89.68231965 7.67369095 98.28872504
48.43603777 80.77911119 56.21494124 19.76545129 75.16244335 67.82263991
24.07119459 37.33099841 42.87237847 30.15264831 36.85458863 21.53863106
96.43944376 78.33920806 63.50630182 41.16601847 80.70726263 85.23955643
31.8303024 96.60302339 27.64100696 91.20904074 73.25605833 91.73509841
95.23782239 55.07524468 53.11036213 55.55214522 79.8481495 56.14182959
72.01827464 30.05308689 10.85024833 10.25895089 58.53811249 12.62681353
27.23885552 4.89899797 63.00084391 30.90542429 6.61767021 22.74349574
86.71899033 40.09404054 36.15639624 30.52767373 87.3345007 18.75623608
90.97469999 57.62612384 85.28866147 21.18783467 11.42831227 60.1203392
12.24772648 33.33328001 13.295221 72.181936 3.54557399 83.1310538
29.28640621 98.63748641 64.50932162 35.50199411 47.36520003 70.49019509
45.42907597 50.83503229 12.99749281 10.20353053 42.61954529 22.86444255
6.89140343 35.00789063 6.98379573 16.99446183 36.79289846 95.60269085
83.09799455 41.97126137 46.77262845 17.75051333 70.21494752 51.15743977
76.887042 46.11431636 59.41986709 85.04112825 77.35457115 43.03949872
20.54671556 71.82962089 44.49536568 21.62760829 96.82990659 42.23815671
65.84223168 35.93351128 44.82495935 42.72675698 37.32449037 69.7798018
98.10077775 80.58095169 99.53742574 95.67368662 88.38994486 51.07061498
69.46742937 98.55541036 5.91928303 54.80482231 93.09584393 37.6895885
6.71679481 76.44499859 11.28000556 21.04530418 13.62523544 15.75788369
41.76021575 24.57391959 52.12249583 97.62899396 31.05473494 4.22217263
28.09280008 29.79519058 80.08876126 3.77691539 56.9815497 84.26487094
27.88381618 77.70632971 87.27456823 74.8118486 21.12475502 95.1922787
83.3654065 76.15523234 34.55695662 65.21478596 3.1972284 97.21260663
11.40552621 9.46093504 17.00562644 4.32369864 97.82594809 88.89825739
15.61001425 49.53367304 38.86859007 43.95620301 86.19930518 6.5693036
67.06153412 52.88815376 41.55699452 70.12818397 55.42928638 11.74089589
58.76945862 6.56570755 59.91851444 83.89393973 79.50888036 17.946884
63.21021254 69.69266984 33.89575271 28.05752806 51.97674346 43.04661112
60.00246565 86.13169657 7.7315244 94.53165108 69.77984574 23.51384251
71.91905551 27.08403825 51.74969492 63.95824182 55.99227449 65.01031161
93.44365517 43.85098778 98.65286561 45.62506792 86.28322546 82.00273308
96.49450314 91.54692267 17.28028426 62.45773925 69.63441861 18.39941771
33.71349805 85.91541687 19.46041828 71.84660377 39.16512299 92.23975635
33.17649781 30.19588847 82.92753736 30.22957691 44.25638795 26.93728637
1.5758626 38.49620568 33.43280116 78.12623498 16.79328465 1.46136911
31.34785798 78.04568659 87.83966173 38.42210924 47.06460091 11.55433869
5.29367573 10.40862963 20.23439086 14.27314342 33.09180061 73.68549667
45.46795173 16.88818646 91.95207159 14.19263017 4.85564635 20.64301138
1.94259568 29.71116535 36.93156159 59.37316321 15.62090663 65.75596984
62.73667776 29.22746689 78.45034881 25.01183979 38.3170446 94.66279922
26.73040531 91.7886437 76.40463902 92.71274349 62.75680744 40.80400081
66.17079975 49.49240252 95.46917633 60.78764786 57.4280919 56.10042722
23.20157611 38.95764541 81.37036948 12.15914064 7.94552897 7.01282573
13.61593231 18.20578648 76.45500723 64.7206533 13.42479268 93.01586101
72.23964661 14.69766014 32.72830147 9.61632175 18.42245772 85.76877221
42.62733416 86.37898472 53.27817073 9.59990032 92.18672745 82.27057694
93.95305311 63.07000703 35.07240975 82.11515802 18.91036985 47.04871513
46.802266 32.6273562 96.63100323 29.37114809 1.64572432 36.27372173
76.7998405 49.19366126 30.70486 60.68419858 73.92216942 84.38451022
80.72298833 60.97759678 64.6663695 60.83422897 40.70568928 8.2521566
94.47596134 94.35937878 35.69060973 55.17212587 6.08224885 32.03166802
99.87379759 80.97863149 45.01542828 22.15663297 78.96475673 80.54019729
70.9690467 81.71962786 4.01691705 24.12934548 57.61605181 48.64575459
11.66663585 88.15355 37.32824864 88.92220588 29.79861472 60.71194514
30.45707293 20.60521384 67.67427627 60.90055774 24.32136198 16.56214825
52.8087451 32.40119943 40.60218556 6.26224155 5.59021409 75.99048999
35.60986943 31.83647507 83.1581112 85.13010588 25.63549502 89.35828897
90.1486012 5.99320584 98.71404901 78.66902006 65.1118605 91.15170195
28.61388527 41.88225479 93.13874407 51.70876069 65.41113429 11.92329907
48.51507506 15.10137171 17.39116468 28.03770426 8.88528717 86.08892649
57.29680683 66.17999644 97.4156697 85.85173882 67.52416924 88.89127503
74.50104518 70.74714956 59.39436212 99.0568475 52.40574324 41.36883892
73.90535744 26.51615386 34.99259686 35.7243146 39.54608264 31.94101265
81.42876891 57.95881308 14.31079343 16.20068779 71.25603626 78.49142114
45.35758565 16.42776125 78.33154812 71.64631202 24.23996822 13.31046578
13.28383326 39.33362647 5.15903921 72.64947608 55.34384315 74.60690975
32.98259154 51.06141677 74.94526392 9.39885721 84.74208688 53.99816379
64.49174602 60.909083 80.74594591 41.52639698 78.9739638 45.76433809
4.79092755 22.91529037 71.26032101 51.29801496 28.65167423 34.5796602
60.20291477 98.92114484 41.70408814 15.8136103 19.99679975 44.6578455
65.12266153 72.122109 21.85128947 51.53564865 63.54676161 70.15032181
33.44892851 38.55359203 84.34026346 85.90465926 19.47844522 84.63878527
60.63833873 37.77186021 38.96675557 20.18214809 29.37537032 31.70313139
25.26465811 61.70917938 24.34652876 72.80296911 66.87810997 86.02804395
64.81361617 12.95192103 91.43898128 5.20879506 69.66706828 87.14992423
92.87322651 63.48723567 18.91836692 73.78443283 94.40584832 44.22557732
96.84274716 88.12286007 84.05322659 98.20144264 67.69127637 7.80211647
83.76762236 80.8625055 33.5542224 24.96538251 83.75285244 75.753899
22.67756189 66.61522576 63.87431293 66.5723809 46.8551844 43.1698331
99.44590106 65.71340711 67.63894111 15.05101609 21.75689224 20.24245942
94.60851529 26.99287337 54.49527204 52.52778543 64.61776401 88.86013739
78.60078864 79.29303797 19.66362688 63.23077722 51.00237491 1.44849486
17.67549444 26.88990168 71.3616512 70.623537 50.52909969 59.9545727
25.72557763 21.00128523 59.61906893 2.32802267 53.2699027 22.87353993
45.07869383 10.95652528 45.33559583 47.93927494 92.81079265 27.89229808
45.64452193 78.0148958 72.18981575 63.92474862 32.54695842 66.86399635
89.14493456 77.67858314 76.3813782 29.99577973 33.71920007 90.20985826
14.70063617 68.82030533 94.84389906 59.20558097 37.59142604 69.57079906
47.95055537 82.2076633 90.92150022 37.57324686 47.75157582 43.516359
48.30594467 86.56281879 62.95788234 27.82168341 41.50806351 53.86318263
4.93989208 62.82831806 55.09707091 51.44336614 29.95804366 77.60113536
61.68202316 95.36510457 37.10468618 50.35371104 80.38828748 12.55810375
31.38106845 89.91978287 16.92054254 35.56945602 75.93417783 68.99280843
91.76388333 72.38444959 35.62321083 80.66686265 19.61220973 35.52844455
46.64414563 6.7942961 99.81263421 81.96845241 4.40092214 93.63426858
50.93438564 10.04546035 61.76950075 19.25128342 7.14283908 87.80062501
24.69862663 2.59909787 67.11358252 16.5552231 17.82910836 63.1271644
80.75872263 88.68672837 97.60397058 51.74553507 11.56246504 7.48690592
20.21984555 2.35635739 94.87656403 86.23631827 66.86763744 79.620118
97.64530482 48.43842572 85.78069896 2.25529827 55.06248933 35.66495592
72.20750027 18.03746937 86.36011836 77.13932452 55.21810808 53.05493988
73.64406008 9.05275724 78.21914985 80.68635008 66.37825733 67.98800313
65.58631445 87.81891616 57.15093449 44.32727532 24.5450758 13.42990955
18.44048876 77.17491018 11.99980854 99.12780004 21.86043415 66.82611533
71.71042868 77.99286701 56.54607437 89.9895699 61.07566637 43.79707342
48.09401621 29.87043251 19.26025971 86.46992767 56.08607985 4.14640582
58.48514412 94.45879027 75.5600441 79.42451128 80.94518993 11.15434534
90.30067509 56.31621528 88.79033073 2.81737437 85.91273321 55.49865592
16.29338532 95.17615873 56.18870202 23.25824216 83.30160155 77.92947928
11.58784647 57.05472495 55.83191139 35.76417333 55.13084236 16.37788042
61.20618556 11.95325915 78.28210114 79.82564279 49.2380535 85.88484173
88.3667329 33.69417258 18.18492189 17.91637699 13.87487997 66.52500776
48.8101565 43.91281358 81.69630917 38.50426447 85.17305697 28.18259994
42.50297412 94.13543642 35.84021426 43.11248399 34.0787535 80.06619629
97.57490266 28.1696077 88.12963095 80.18606584 72.28095937 43.62203319
90.56351229 41.77992114 43.69253787 44.73829527 65.18867355 60.2747685
66.81760249 35.45803367 58.28328923 26.39514097 98.12896785 58.05592033
94.24998803 74.50468867 10.44670771 9.65383881 77.35914108 21.86123538
82.51400007 49.72754903 96.9867392 90.51251943 22.13992217 74.03317205
44.05314033 33.9529891 38.45572635 85.544268 7.93725863 16.29981858
88.83099801 58.92816795 45.11954098 68.94748972 61.90757593 83.87751155
61.75143191 64.27218474 4.95890226 99.05690529 1.91073107 63.82253912
83.03639838 45.28693023 78.70747134 53.62440458 41.42327016 63.45915853
70.44485585 11.76294479 82.95248729 84.54279505 66.49324469 22.28747942
1.35066193 41.60488581 39.1499989 26.36834323 44.19543993 43.24516398
79.01820291 43.81613998 68.24656691 40.48999844 86.97347868 65.22400182
92.23655129 18.31260382 73.37802402 28.4535868 82.04877542 93.32146884
28.48732721 58.52761609 90.18588667 40.6363922 55.29529527 80.43103269
60.05819482 55.22515358 45.1087248 97.54449481 13.59435216 4.36973903
83.43294516 64.07082262 14.67853182 63.48225747 96.79909808 13.15552855
49.9620672 6.13443299 17.8734181 78.85694166 25.13578427 40.95418209
66.60594127 82.63723925 69.37803172 73.84693231 76.38271067 95.46205065
88.26455536 70.00960993 16.98388486 43.95925623 80.88974698 88.93347061
43.66894866 8.9675425 19.80329028 10.57411784 86.16195289 3.24662912
72.10374876 37.42091596 96.84238033 66.99799427 27.35054862 98.12178429
32.73085626 24.24130565 83.60963339 74.24491586 93.58519264 27.96094989
44.56773073 40.32835157 87.46139432 99.13158899 5.39536168 46.82397805
40.48837422 73.39351715 96.6101856 32.04336295 93.53084661 44.83836999
83.18821218 34.84316917 53.07064736 83.30908724 84.51695306 85.44334485
93.85190508 80.7717744 85.78154731 48.12811636 89.33351337 70.48590974
85.62088937 30.36880118 45.31857277 16.16489924 41.99671998 50.25968317
66.8636397 16.10985049 69.73479179 69.97084737 88.23869534 42.19641241
64.84671436 48.04093875 16.07649392 59.94968451 76.46746681 86.03116423
16.76892529 29.39983201 32.96910423 6.22133615 55.75296427 98.57778915
33.62138919 42.95220304 28.92439411 83.86415015 86.93923401 48.52103952
25.86705521 93.93802788 53.59553216 35.94664812 94.28193972 97.65209481
25.88674735 55.80523164 19.09496336 72.03812924 85.64096678 75.9911182
71.11120523 93.14856568 74.36277665 4.14481733 24.25328959 38.37227362
17.552863 45.51022589 53.21778801 33.99353608 79.36764145 72.16470323
91.33261186 70.22669975 24.39604327 44.54672385 28.07524626 23.22051292
53.53690011 79.77360749 69.82774806 24.61844959 23.01819973 68.19884677
43.69581277 43.55789449 69.57822241 95.33189115 33.25973 36.07121273
82.69182936 72.19343459 89.26463538 24.8442276 48.59642659 46.57813846
50.95500429 56.22906289 24.46109729 1.06681722 3.11446767 84.3696025
45.95153857 20.98741929 73.54870699 50.7218902 61.25690785 95.48062951
99.55185393 54.49172367 14.08941178 13.74135919 94.32273562 5.74364549
52.94220473 28.89203266 56.10023689 56.68143607 54.57491497 23.79944835
21.12197648 1.99111745 23.43354189 61.57383934 88.44655616 47.95251678
45.3604372 27.50908935 44.42129594 62.9973951 6.28747188 69.37653273
76.11954533 50.37553642 30.63549911 70.15490486 44.44411625 75.99535003
47.27156406 81.73057713 21.22266131 72.1981913 ]
# generate 1000 floating point numbers normally distributed about a mean of 50
# with a standard deviation of 5 and make a frequency histogram
x = np.random.normal (50, 5, size = 1000)
print (x)
plt.hist(x, bins = 5)
plt.show()
[53.90789169 48.23264624 50.35391597 43.97274727 44.70625273 48.9884623
51.39143925 41.01532299 52.90561698 50.95261908 52.66049296 48.80866564
46.83503841 48.16008929 53.66307231 47.57394539 51.45126089 59.04981197
46.79037724 52.28206952 46.00383057 47.61169703 48.78845228 53.80491351
54.20153528 44.98524005 46.44067628 44.52668982 47.94441426 50.21266185
51.58446022 52.16075291 49.10288554 45.83353068 45.72452247 47.87244444
49.77839417 39.52086772 53.0664182 41.50163263 48.75308134 51.78868242
45.28018241 54.68395395 51.02686506 49.27543271 49.43805594 45.74658668
51.08806383 56.14750226 47.76272229 46.06605477 49.42139025 50.7874248
45.08199288 49.89983889 56.33442484 54.52800491 54.88114633 52.90663407
45.92645021 52.2533287 46.6678836 54.28304682 52.30725753 64.15775433
50.90358913 60.26129915 52.98273071 52.75953548 44.81060105 45.85441742
46.8367313 45.74625044 54.75794717 52.62954657 50.89853439 57.60953039
40.07724341 48.8960352 47.64248705 45.92530841 52.07915501 57.93360381
53.00319836 46.92520968 52.9653935 50.70106971 50.48933439 46.33937371
44.86563838 49.72408872 38.17535939 53.65483286 58.46368993 48.41941512
46.34606318 41.65898317 55.58088727 45.21352582 44.05873217 47.13707567
61.50738548 45.8791115 49.21831579 58.49612498 47.96093747 48.54237215
55.4107038 49.77084601 51.13688868 57.71408532 52.11369041 51.99466876
48.02447223 49.22101621 45.62974322 48.06567664 45.81236136 55.33225124
56.89063771 41.19717432 49.33212048 42.82811113 53.54410958 47.65051222
42.218634 49.39816755 53.56880101 32.99373926 44.49041503 50.78160369
57.32650331 54.02141039 45.30143098 51.71831464 54.53691796 48.04377308
50.31180747 56.62528207 52.09350128 43.8709268 48.97303013 50.99297291
56.71388657 46.76577333 46.67711126 52.63287494 43.96218302 40.15559001
46.07642003 52.18566041 54.54572267 49.13740777 47.70319524 55.46005314
43.42319306 50.49212503 50.78384473 49.73627887 41.8049758 49.30513529
48.25740452 55.18237697 46.0452265 53.56076875 48.71545224 51.31548563
49.91109174 52.81148842 51.47892689 46.0313482 51.25036288 48.44878115
43.62108261 51.99545873 44.18528398 51.59350331 55.1514299 56.85836719
47.4620901 47.58556022 53.16152194 55.12551999 45.85821765 47.77647496
52.63559131 44.18480598 39.99061342 43.11776961 40.62855822 49.16868447
54.64884303 54.30013774 52.54743784 54.61500886 44.5907155 55.53791371
57.09806277 54.36093467 46.77721271 49.2814248 60.50827964 46.73611426
49.33063324 55.70759756 50.17389329 55.43168547 49.92991434 51.56959826
56.77143379 50.08853824 52.2034544 43.09491907 46.68182912 49.66560242
44.88050399 55.06456427 44.70989211 48.61147156 54.04996831 48.2910573
50.2454689 48.60673106 49.17851067 45.19561808 49.77991026 58.41178367
45.93932686 47.21058771 35.27537664 47.58318736 50.02813332 49.52863301
47.91988937 47.3775753 53.23378494 51.95725348 53.51055456 51.81576565
45.33003241 49.37080666 47.31660517 46.21915584 46.6510461 50.94150338
48.93372452 55.80838983 51.54956255 43.89855104 56.87288778 54.74669636
49.5390731 51.36883682 49.17949523 48.44295958 52.00911136 58.63631914
49.40016961 49.77952643 55.65956142 49.51900986 60.03302489 49.61761394
56.61240703 43.64935463 57.34684495 48.18289933 50.2711123 51.38134042
48.40639106 58.93258837 50.1867699 58.04212689 36.90102693 50.44977997
59.11450339 42.04587715 47.25913084 57.72271104 40.8363 42.16659202
50.02052972 53.77108433 45.48064283 43.1871799 50.47291913 58.66355059
53.18459766 48.62612195 45.41400119 47.39385059 53.58139664 51.10263975
56.47378075 51.52581547 50.09347653 52.8995755 41.13351076 46.52151154
50.49640493 46.29682364 48.93765656 47.59285785 53.05306123 42.53315842
48.51259505 53.84324813 55.09546022 53.45752263 54.3293361 54.72716098
57.7114943 43.82603158 47.59285139 48.13647623 47.03919834 57.69721345
48.60277521 47.74660766 43.28123849 52.39207594 54.16933087 49.96108292
55.48097743 47.97469323 55.2590924 50.74132947 46.70346056 57.1975321
51.12574866 51.58773736 48.41426034 51.736925 54.92457082 43.92939388
44.25336498 42.68811539 51.03087758 50.48458562 40.09445374 49.3201426
59.55544023 48.69816665 52.17419273 59.81120508 43.25538049 53.07181269
51.13745032 53.97240024 48.37735011 49.71611082 48.12543187 45.86559787
45.04688366 52.33862738 45.63695844 50.52026459 52.01369294 49.71748202
47.59630917 48.76178672 42.55630028 49.81562296 51.79734941 49.53890007
39.07083418 43.33916923 44.71668775 47.00041561 52.84717993 52.64153455
46.77669955 45.93922885 52.97024565 46.47977099 47.56766288 59.56780688
44.60847537 52.10901586 49.91606142 51.9829812 49.77887017 53.03460532
47.56248567 38.12901609 47.56523568 46.79420365 62.76705908 49.84604958
46.36849804 44.7608249 56.01322634 49.42223835 43.20900363 52.72291325
46.2770407 44.61133369 46.80327021 56.47410375 46.5049597 54.8123064
49.52365851 48.09312132 53.53660734 42.30279243 55.36990789 39.55789051
51.89735263 57.49428199 45.94461467 51.17115132 54.24217678 53.35474511
53.18844123 49.38371543 56.95595379 48.77227998 46.26069841 54.4715498
50.2364661 52.59866811 62.70919793 49.21614434 50.26839342 51.00590074
47.44505756 45.42612659 40.93483259 57.46147696 57.14060202 43.69779301
58.26073072 48.4828026 48.80867947 54.17205299 53.58915397 48.34310787
51.15305769 48.26572519 56.38527446 42.47189474 45.88577644 46.58671646
47.33806455 46.26825786 50.62488729 39.85667901 45.92704734 55.96727319
49.5911293 58.19496281 55.43697003 52.63097221 51.954234 48.30009541
47.43712151 49.00113211 46.73007937 45.44356993 50.10725302 50.22295985
46.22107779 49.7906971 53.54600086 40.91975625 52.92582487 48.35031906
47.36871138 53.1214928 49.9842477 42.15893412 50.46676664 58.64066905
57.49230738 49.60831932 46.78124319 57.31580294 52.11510299 54.33634826
48.82035746 56.58926984 49.22126025 46.88485234 48.17613878 52.03366319
46.4533123 48.89467672 45.45075864 49.09161376 48.79197921 57.95541144
42.45343186 41.34369919 47.54800251 51.8932929 48.28429238 52.526447
43.87824227 51.11118822 52.24514417 45.94521918 53.45023963 53.42914065
47.63218261 56.52029737 47.58058017 60.57291404 41.36575403 50.73681437
47.58928908 46.51424625 47.71090492 46.48179339 53.3016019 49.50902557
46.91208965 49.84578209 53.28308511 43.78317339 54.93504932 54.58391977
50.35117569 49.29690627 51.88640533 60.74063632 64.84594474 47.97114506
46.79790718 44.82749431 51.72592419 55.38364799 45.65656958 39.12276045
46.92174357 44.82791454 52.42783088 51.63710474 54.98174119 53.81677857
45.85943565 40.10789602 46.24477 50.87627022 55.3211485 52.03607784
51.72375857 57.61217097 57.00231236 43.17070047 57.38714637 53.7744477
47.7163192 49.68504018 48.14423163 57.55950776 49.9666456 51.42509075
44.10975274 55.33789826 42.01672186 51.85699982 51.21011918 54.73636353
46.58081351 46.20399202 54.32164133 48.20679411 54.27560284 48.49042143
48.84617651 51.94269007 57.17486895 55.51176991 46.21160981 42.59755403
52.10894465 51.26861052 57.29787498 47.81928634 53.0896867 56.2702396
44.35671986 51.14838985 47.85781984 50.15338912 50.52301954 46.15250602
42.21679137 51.98799313 49.96274518 48.5049731 38.72948385 46.18377701
49.89753557 54.95958226 45.44821236 46.61263279 45.0171647 56.45924568
54.78267808 46.08629126 54.91583673 47.5208965 48.54590181 50.70828205
52.16534037 46.54360924 49.82578662 61.21608741 48.91563005 58.99052375
49.55326651 52.95215865 49.46422717 51.08338318 54.60810492 48.91862689
47.00342495 54.13619414 52.81017969 48.02593697 57.10401274 52.00325757
41.57050573 49.53414476 53.88738049 41.50438845 51.74784024 43.87224645
56.1772098 46.11278098 53.34798571 45.44096731 46.20297825 44.93127965
50.49606485 43.64965528 51.74415566 43.3716168 47.62837761 43.40221085
56.6114911 45.8677984 53.45425111 40.95017947 50.22560806 51.56216018
41.80965335 48.49751481 53.76052561 46.3049327 43.77093938 46.17299987
56.58411818 45.56102602 54.11814185 49.74155855 52.24181338 53.14900279
51.12498951 49.69943231 59.1377249 48.5812284 50.10718217 46.30668679
41.37788094 49.30477409 48.02790807 43.3250477 45.0168271 53.75444111
46.52455088 61.97652121 51.47386709 48.32964567 44.78146046 51.73345351
60.37959579 50.24127643 52.63066007 50.6429086 44.01488078 55.36809973
54.44365485 53.92789018 48.24276302 49.63734382 51.60203976 55.30184484
50.8795324 49.46142693 39.30022582 50.53953478 57.10843871 53.01947234
56.95029209 45.11309319 56.77460274 49.25069421 51.23157015 53.18993845
51.88292495 44.96851382 48.75785457 45.95420065 54.37387365 52.25891598
43.86794571 41.58591109 53.7022285 48.03025597 52.09138904 46.94244277
49.70671974 45.25546226 48.16410135 50.80915462 54.22564237 53.01950662
57.73651073 56.41928397 46.63961128 48.10237313 50.72549368 49.93107606
43.6654366 42.33441826 44.31618196 49.14474425 48.6750413 51.66448934
52.88147775 49.41977622 55.21093158 50.79363866 47.94158472 56.95477293
42.49104268 48.34296288 51.93950803 63.50033274 54.73258353 48.21947234
50.30863315 49.93428118 45.42120848 49.16231702 57.59532706 50.53417024
42.79211125 52.66894576 45.51101276 50.64619933 44.94877141 49.34019273
54.19651009 44.2555325 48.95409276 45.07765607 55.70309778 56.36725327
51.43214562 46.92701073 50.73846429 50.7406075 43.66595684 45.42881988
47.31739062 56.75601723 50.73938915 50.51678438 57.17916784 43.62462496
57.79918232 54.40807232 49.91485982 52.9316344 37.06224906 51.28413421
49.18768916 49.13964266 48.22025713 41.24995635 56.9860087 54.99106253
48.85269174 55.69067053 54.76193823 51.77625047 46.78636851 55.25512325
53.04464129 50.46299977 43.43346974 55.60125231 45.91536494 45.89306087
48.67259833 44.93096996 49.39752255 56.64131844 49.9844188 56.80197551
57.27123964 47.69038752 48.82564061 54.78287371 46.32180277 45.12944825
46.31870837 47.04187148 47.38449366 61.7582543 57.01768386 58.25193011
45.67442457 52.98318234 42.48458019 48.07647417 39.96161665 46.30327177
44.07442533 52.9077175 62.55393753 58.54671905 51.96248667 63.24920002
49.24394941 53.11375813 44.176048 46.68062054 49.77537487 58.95137399
51.21098187 58.34431559 57.2445106 44.00338144 50.68755788 39.32276217
46.69626436 42.43536639 43.80090028 46.29683052 45.66516676 41.83055298
61.71348885 52.77504023 53.43690224 49.18713304 48.15914299 48.8663257
60.1162965 53.18440439 49.78452609 51.95160448 61.69639915 62.40725739
52.79844783 49.50394294 39.20301361 50.76337087 48.18394556 44.98378785
59.72222114 53.33101213 46.86962854 43.37140643 57.1649115 49.58198237
49.33522862 54.64106571 51.68650365 56.8528879 56.20395092 48.86624635
58.27035747 49.22676429 56.17904226 44.66120517 51.15560672 49.77343888
48.72126902 50.30600824 49.31576655 54.26730758 46.22220222 52.28082906
50.4643581 50.05022811 44.59527013 48.33910919 54.15545625 48.01416235
49.9527022 50.21963599 54.08671512 47.26767325 50.54701122 50.46699072
46.70278845 50.61146202 44.8384234 59.35154325 53.52200544 47.44695399
50.56959296 55.30340111 46.15299094 50.06935983 52.11941347 42.41375698
39.12374485 43.03369954 49.73894239 40.73592756 43.46339721 44.25085346
54.60631965 47.66169986 48.86385925 44.07793897 49.53344362 50.71308049
48.77934728 51.1681686 44.3955922 47.02917024 48.73359463 46.9897998
58.21649191 57.25003046 52.29020506 43.11355733 46.64764714 47.48754849
46.58354758 51.01093515 52.18289336 54.52795947 54.28402839 46.44984619
53.76221095 57.3097335 42.51228566 47.14383665 47.27718341 45.81558064
48.68726097 53.86474278 48.23777617 46.24846918 49.07755532 42.95237861
41.01189289 47.1949585 52.27822782 47.16705563 52.51524555 43.00838556
58.53002677 49.52466846 50.31275755 57.37405382 43.16267808 50.62740426
61.49999921 50.81957074 49.40355022 52.92557093 51.11879985 48.15288956
49.57844429 53.31390348 47.80367504 45.04570758 48.62540711 53.149007
52.72475025 47.8022984 49.72445966 51.14024191 59.12751146 48.63022112
58.01941045 43.51215264 44.82368148 47.50991274 45.14658536 47.87609362
46.56772739 47.73745186 53.77747558 57.44046084 53.19850952 43.00686455
54.9747478 42.97431357 50.52752086 50.61168984]
# generate 1000 floating point numbers normally distributed about a mean of 50
# with a standard deviation of 5 and make a density histogram; compare with frequency
# histogram
x = np.random.normal (50, 5, size = 1000)
print (x)
plt.hist(x, bins = 5, density = True)
plt.show()
[55.67645639 45.39801707 54.9417716 47.72806548 52.89261722 48.43641788
47.94107728 43.4486811 52.77292782 53.64369942 50.1852409 52.49713063
51.6597478 49.16090066 50.52112944 54.81465834 51.88992514 60.62819977
53.9979013 48.56030612 46.64114583 52.76215371 57.58022943 49.048392
46.80485283 41.21888493 49.63907911 49.38174092 49.63348071 51.81929695
53.16359775 56.0723027 49.7703143 48.02731859 52.4977246 55.92886455
46.21159181 49.07534084 48.9560476 45.73871548 59.50862888 44.13755011
53.25267079 48.24171858 54.37080532 57.84390084 49.3544617 40.96759653
55.34119849 59.83617718 53.44583326 43.03492722 50.71552169 37.90071974
44.85876402 46.49832056 45.39222673 56.01093301 52.40591546 50.8489851
42.1691961 41.18125406 48.25906722 44.60927161 43.91618096 48.7556633
51.27482293 45.45332971 50.43206138 48.43695384 51.5373864 53.93908756
53.94722846 38.39918573 54.34910201 46.24804796 49.26045676 38.18466772
42.59411802 60.11145657 49.35877261 43.93260203 43.14521 57.74790437
53.50659842 51.52613332 51.33215212 42.22712075 46.18316998 46.86939357
55.66762974 50.2725622 49.54977066 59.07262191 51.91773857 55.26592484
53.64942181 56.68151563 46.77694373 54.74191491 53.08662106 46.75503075
53.63271602 42.35062549 50.05608626 39.19963494 50.5282899 47.47545089
53.28952636 45.98780841 57.1162092 52.56698593 53.54323238 43.90375271
60.48438317 47.43553228 46.9392818 54.11573664 39.77791593 43.68810373
53.40860797 52.01579988 48.37199688 53.60452623 43.7225854 46.83172151
51.24662683 58.25314703 40.85391925 53.4136894 50.25389005 53.23645407
54.43476679 50.78113796 47.98851309 45.95253368 48.67572349 47.19067026
49.88942162 53.35874833 53.21829464 49.00190858 51.70212693 44.56202698
43.55839653 50.25063219 51.85634343 44.36921567 49.36641185 47.26115623
52.373133 46.03983933 50.43943144 52.32283163 41.34177819 54.88939413
56.67441502 53.88220867 47.05883024 53.44425647 54.76248875 56.8129662
43.41216202 48.33335906 46.24535961 58.82395143 58.29436384 45.29097696
46.22133313 54.79254208 39.48716008 53.33173451 52.98686302 48.83973856
47.520404 44.23959903 50.66086206 50.56990008 52.57805617 52.82315808
48.44331284 57.50259474 51.80203823 51.2869197 45.88528221 46.46845371
59.0221497 47.98543048 48.5287019 50.39501747 59.2383767 42.06624852
47.30466871 53.59245153 51.57018682 54.08010032 39.2255643 45.36452148
36.43221367 41.27838847 50.71322805 54.10161455 43.49711427 45.76842812
42.71328864 46.86808283 56.47187338 54.83198592 46.93293846 48.96276972
55.30250415 40.47181144 45.49621227 59.51591571 53.46624946 66.84167405
42.12233191 45.94102098 42.92473014 53.23935316 46.06527734 45.39058168
51.64940388 53.2887935 49.87423593 62.68593238 57.09605295 44.93339864
54.93982913 49.65225205 49.84688277 49.87577569 44.83754918 51.80484388
53.09875203 52.00494639 44.61664377 36.66275164 41.61696146 43.0489555
55.2441524 46.17010625 48.27473888 44.66424419 48.01492263 50.42310873
44.27531394 49.0845317 44.41692835 46.48054151 55.38184556 50.14498146
48.91811784 44.53104393 41.23876771 46.69862474 49.41074497 51.41603424
45.76961511 53.20843472 50.95759141 49.46298452 50.20081856 45.07388306
54.68157058 50.75821688 49.85100026 47.70048663 44.18615191 59.73665748
41.89453801 46.75412766 44.43527087 63.41460903 48.27341606 56.06315863
47.54588353 36.67854874 53.67614511 49.28407361 42.51180908 51.01041334
48.94723049 51.59576148 54.36772424 49.11384435 47.38536795 48.7145328
55.56457632 45.70201783 46.85517604 50.75599944 58.05038159 43.37462095
52.38325464 45.86267828 54.15053553 44.78309905 47.04442609 55.81009784
48.71836957 54.43621458 48.91840911 48.47162812 55.93493599 40.22620819
54.81085001 52.49729743 45.37894941 50.14396494 48.24283392 54.51394465
44.78174355 51.40695068 50.0618733 52.0497046 50.0049361 50.55316125
56.89061986 47.93312086 45.9090708 55.3634327 51.27915849 47.18441101
44.62583893 49.11150426 54.84323209 47.99969564 46.06402259 48.34634619
46.13536009 59.46890552 53.180752 46.54535658 49.40087778 52.73142381
47.76788661 51.28043483 49.79790367 60.2472857 47.16830987 53.03747337
46.3964626 48.62477765 50.19302153 55.76056925 52.69298352 58.81694205
46.04069037 52.37308753 53.31910245 58.52080681 40.98581562 50.6795186
48.20605579 52.71973811 51.6326748 44.68315344 39.89380176 51.32702948
43.36214122 50.68985372 59.64034772 54.54622844 48.48933779 67.08447849
53.69488985 51.92521324 53.28697234 47.53250449 50.48734339 53.55955965
45.11619949 58.44848286 43.44546058 52.39315674 50.06275872 46.91303679
43.90538971 61.26398523 52.22925164 48.75736231 45.91385134 47.06380256
54.06850799 52.29348353 49.31949094 53.08342638 54.52331657 56.96286158
46.74942169 43.81257997 45.60402374 54.72836183 42.95805331 49.26197067
50.96791591 58.03102217 50.7360535 51.25148949 49.54636969 46.99609342
45.40261933 49.66828112 51.98843252 47.91492013 40.98112952 51.47610396
50.64263404 55.26292023 44.99877998 52.54768755 52.26435981 56.34692083
47.91924806 49.23929762 49.56514486 47.15226197 53.57777872 40.5482454
54.33849518 48.81075089 45.77690916 41.4075578 47.31327847 48.11708757
47.36624793 46.12292096 39.86656408 52.23803487 46.78064903 52.89797558
46.61605924 48.94453647 45.5655497 45.0466073 57.62980393 46.95512714
53.30634503 58.09293507 48.38180194 43.67014256 48.2876625 57.25973099
40.61663558 54.76936558 55.42450985 47.90593892 52.06211042 51.69259028
48.79743995 42.9572874 52.13026274 46.1044758 48.66008776 41.38672425
51.1258164 45.62743015 45.84470424 44.80308204 45.21784198 44.80953029
60.33650016 53.04812105 57.53824248 56.47684963 47.34481854 48.34087921
61.48144357 44.56194547 57.27800809 47.77364864 53.075318 44.2484724
47.11628605 51.25896624 42.54058326 48.51458714 53.81182886 53.72733514
41.38055073 63.89404099 61.69060876 49.69852526 45.900292 52.7145537
57.72863571 44.11491048 60.97239444 42.55323956 44.87816646 49.05095085
46.27858415 50.31355415 52.11220132 47.49662909 50.96713985 46.2629014
51.54214233 50.1979052 59.58701771 53.22967657 51.93746755 51.03526219
47.90547886 47.27740279 53.01951284 53.63645238 48.88808662 47.02757423
58.7859499 49.2969145 53.33771038 47.4220013 57.36859442 50.74109804
58.46891794 59.97519105 42.93318034 45.49429147 48.0760432 57.74845366
58.16899009 50.6489172 49.84942409 48.06025996 45.30128797 49.99627886
52.3590615 50.94816213 50.56430806 48.11364082 49.96864971 59.52363787
46.52302955 53.21039563 52.4703776 53.06671883 51.61751632 54.06467085
58.42343355 49.82916934 50.20654404 53.91894766 46.72033421 41.01140289
55.6113572 48.74769028 58.76362351 50.24599573 45.24116779 47.18475311
56.67633482 47.95895741 46.72801155 56.43318743 47.52162464 48.19233219
45.93727659 48.69557367 46.01285631 47.42321862 55.41166493 44.23232669
57.46739787 31.94750719 45.19990137 39.23699193 42.74399205 53.58366612
48.10024511 51.74180601 58.53028825 52.96623945 46.17514087 50.77187841
44.46971131 49.59595086 41.19228894 45.26090643 55.54686131 52.77681937
47.11077183 54.06500005 49.64228551 42.3318984 47.95627337 56.97547554
47.57003182 48.25347861 55.83833842 58.8321409 60.56248376 43.46280726
44.34297468 56.44612833 56.93929416 49.0094076 46.61211447 49.8865142
48.5553811 52.01169304 46.68747035 47.81821156 54.47696291 59.97751162
60.13292085 47.13895685 51.03045514 49.34728254 51.64039612 44.38585866
49.16730146 49.23838953 50.63555952 40.63425619 52.02167405 48.18444906
49.87323119 42.74460736 48.35896733 52.71425451 46.6212079 48.69003821
50.2311103 52.61067934 39.70941864 49.23598048 51.12948066 56.86841989
38.74935166 46.54629345 51.73864446 48.09217536 44.57568036 50.7185047
46.82593168 51.21532111 49.22942868 45.5999051 53.53207294 51.70950068
53.55171851 45.86502116 47.41811445 54.74025082 50.42102228 46.89637009
47.01001992 56.57886411 56.63633382 48.29095045 50.60123325 45.92174337
51.63281112 59.46616409 51.94936643 53.23367721 48.85901137 48.6260891
46.23562973 46.58129064 45.17261884 53.0423151 47.5864637 44.6111568
54.92424881 53.50489169 58.19540557 56.42186938 54.10554485 50.50030503
61.72821005 48.01638653 56.08427792 38.61584768 55.42816572 56.86930283
48.3830178 53.00327377 53.01177988 50.03779096 48.839495 49.03334782
52.68792751 58.24776794 40.47364194 47.86286424 50.78225163 60.17571157
56.94533631 50.45459844 41.10394822 43.10327946 51.64372143 56.66927966
41.8945852 46.65074137 53.96563709 52.09176758 56.21452147 49.32113303
41.93024155 54.7773917 44.28283456 49.89684853 49.99248289 54.8789269
44.10336926 46.83626691 45.67978329 51.20352971 53.38590698 61.05199209
48.13026433 47.0339645 38.74013274 49.13900171 40.80277996 51.01385728
48.13305068 53.75107256 53.52007282 56.97369304 37.32683575 50.75838772
46.0444552 53.0100391 39.07658059 47.63875096 50.11407635 46.13247775
53.57614537 57.20678842 51.32872192 48.28614875 48.40278904 54.9018374
54.7631185 42.49034216 41.27942487 36.77980621 53.22064995 52.65443333
48.43991502 41.79561741 46.25157328 44.00678374 53.27428284 52.11084357
53.37262545 52.1708614 50.18240098 53.52080032 53.91378273 53.6249963
38.19767522 53.08690517 47.50143569 51.33389144 48.95317215 43.87994406
60.38593407 51.66939931 52.01058898 51.31321438 41.78605921 49.83813573
50.03940759 55.92043805 55.80069467 55.86648538 53.26856085 47.86684169
51.79686384 45.47688375 53.01330305 47.68045371 52.00832914 47.73019884
49.98197405 50.37777251 47.22830532 49.59066397 53.2831387 53.23308247
48.19004552 49.39166163 44.23934933 47.1935526 48.62469993 49.20986994
56.13326562 50.90440091 47.48269766 58.00954388 50.73271939 49.67040783
53.28152983 56.21594859 52.41949394 47.43856919 45.63637621 57.61205496
50.40297232 41.61966738 52.17901999 52.22866861 41.75269493 50.84830246
56.23090265 50.65841125 39.99006132 43.63488641 54.35250815 51.07291275
50.44225987 49.13317891 56.03732884 52.73060362 52.04757337 48.44742308
52.92506889 47.5473593 49.72680477 48.80387131 53.5054453 51.14328225
54.40359744 49.43831692 54.06947459 47.29154541 57.46974611 45.7919625
53.47424059 57.37741631 49.47865574 47.27051729 50.10088919 43.4691524
51.93942471 44.52721759 43.10041087 57.87349393 51.17452186 43.31456603
44.99288451 39.52802033 56.89247478 58.61560282 56.72558818 45.29762522
50.03726039 53.37538492 52.45814082 54.81180292 58.6861227 52.04905601
42.00767428 49.30167918 44.3638898 48.0893597 53.09244763 45.72679255
51.00331613 57.23652531 53.75524127 54.01387966 48.68365606 42.7021285
46.62617573 42.36073446 53.00296407 54.33268468 48.30480777 54.94431372
49.44069453 56.69336287 45.32037391 51.1102511 43.30480787 48.99087379
52.92036396 52.28252566 49.54393044 42.44476064 46.79771877 46.21614364
42.28899094 49.45482941 45.46925822 41.40486891 51.37852095 59.56466612
42.94021653 39.00854515 44.81464792 47.73777243 47.57670084 48.33927481
57.80694091 54.62490218 52.0903013 48.94788402 50.9487047 53.12723212
46.24409494 53.40816775 49.16983528 45.92311867 59.82502422 50.87040242
42.43238901 55.66795973 47.3068575 53.22310497 51.69792864 45.77336744
56.46778281 55.26405932 59.84573297 50.86398643 42.5928792 50.28092347
48.29801246 44.21105543 49.54077232 53.027715 56.21582621 43.67103014
41.39782395 46.89799654 50.37781285 44.84845859 49.17379809 57.24117596
52.3571868 51.04835063 51.87747356 50.77297091 53.49869642 53.23169769
42.49103047 55.4550146 47.24776642 48.85287287 44.48134234 48.41711089
46.21382726 57.83950408 52.3741423 57.25854241 44.82359516 44.89169178
50.85404551 48.04003238 53.9088812 45.14792056 49.64103483 54.98562046
50.25085181 54.23966989 54.90628829 44.16280231 49.75171548 50.75713241
53.48525422 54.38714399 54.66889575 50.10462912 53.0098605 57.35241032
48.53094648 52.99707792 53.38098522 43.16935039 64.21862366 48.72710646
47.57140689 48.53375686 46.13129324 53.98921306 51.14130797 51.24942795
54.42644532 50.18568258 39.49179792 51.43192805 53.16804645 56.21076823
56.88287295 50.09121415 59.18896489 51.74025518 49.79897657 49.32957686
40.92271255 57.23987696 49.4239665 48.9732643 ]
# import random and set seed
import random
n = np.random.seed (123456)
# Simulate drawing a single ball; each ball has a number from from 1 to 50
x = np.random.randint (low = 1, high = 50)
print (x)
2
# Simulate drawing 100 balls and keep track of the number of balls
# that have a number less than 25
x = np.random.randint (low = 1, high = 50, size = 100)
print (x)
k = 25
count = 0
for i in x :
if i < k :
count = count + 1
print ("The numbers less than 25 are " + str(count))
[43 44 48 44 28 33 24 37 9 11 11 13 12 21 44 48 23 39 35 15 7 43 3 48
5 31 46 24 21 21 46 6 24 37 12 36 30 40 17 35 19 16 48 33 28 21 18 11
47 29 21 15 13 37 22 47 40 8 32 32 5 2 43 5 18 19 38 20 13 31 29 43
26 3 36 10 29 49 4 33 38 5 29 19 43 8 46 30 18 33 4 25 40 5 45 1
13 37 49 6]
The numbers less than 25 are 48
# Calculate discrete probability that you will draw a ball with a number <25 using 10,000
# simulations
print (25/50*100)
print (f'the probability is 50%')
50.0
the probability is 50%
# Now suppose you are playing a game where you draw a ball. You win if you get a number
# <25 and lose otherwise. Write a function which draws a single ball and returns True
# if the number is <25 and false if it is >= 25
# Test out your function
x = np.random.randint (low = 1, high= 50)
print (x)
if x < 25 :
print (f'True')
else :
print (f'False')
x = np.random.randint (low = 1, high= 50)
print (x)
if x < 25 :
print (f'True')
else :
print (f'False')
x = np.random.randint (low = 1, high= 50)
print (x)
if x < 25 :
print (f'True')
else :
print (f'False')
32
False
7
True
2
True