# import the library numpy as np
# import the library matplotlib.pyplt as plt
import numpy as np
import matplotlib.pyplot as plt
# set a seed for your calculations so that they are reproducible
xp = np.random.seed (1234567)
# generate 50 random integers from 1 to 50 using random.randint() and make a
# frequency histogram
h = np.random.randint (low = 1, high = 50, size = 50)
print (h)
[20 7 6 35 33 33 14 15 27 36 12 46 49 3 6 28 31 48 20 19 8 37 40 23
36 34 33 24 47 23 21 43 39 13 1 41 49 16 42 23 13 26 13 38 16 41 13 40
28 21]
import matplotlib.pyplot as plt
h = [20 , 7, 6, 35, 33, 33, 14, 15, 27, 36, 12, 46, 49, 3, 6, 28, 31, 48, 20, 19, 8, 37, 40, 23,
36, 34, 33, 24, 47, 23, 21, 43, 39, 13, 1, 41, 49, 16, 42, 23, 13, 26, 13, 38, 16, 41, 13, 40,
28, 21]
plt.hist (h, bins = 10)
plt.show ()
# 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)
[31 16 40 ... 20 37 37]
x = np.random.randint (low = 1, high= 50, size = 10000)
print (x)
plt.hist (x, bins = 10)
plt.show ()
[36 48 48 ... 34 15 32]
# 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 = 10)
plt.show()
[73.32556734 31.34415826 44.27082227 91.87999662 8.58579447 2.03457655
92.57002939 15.06822349 5.97487714 39.2116337 65.70408974 26.9763669
66.73732544 82.25878927 63.36768864 67.54378546 14.37481024 41.27567692
51.14869755 9.07546129 37.39185067 59.31186542 88.11389329 16.50446606
70.60371461 67.45850787 86.34713116 81.59450775 58.10011092 59.32721109
62.73486512 73.97339341 68.67705542 45.49894859 57.70557681 55.65945498
56.17206745 11.38002695 69.36503304 95.13908918 18.21157439 58.88110174
3.13531272 14.66134222 89.33694101 80.28812728 80.89728797 57.89236376
46.17061698 2.58406156 73.31272368 81.89171791 20.87184216 31.9244392
3.90498841 30.42903521 65.87820878 39.39613529 58.07454494 17.62821302
3.44628333 61.9519944 64.83863499 77.44356755 66.90505184 96.62447053
96.97647071 79.34848682 74.65091356 17.60063002 53.18480152 84.16721972
34.81736841 92.94590868 39.13282808 37.60716242 34.84494462 28.85651184
54.66264447 78.58237705 75.36207709 28.09935159 13.60586864 75.35175675
23.95540595 27.02815057 6.33505492 26.4290108 78.74267619 77.0153832
41.29759949 54.28089679 2.40361885 1.38127748 84.41804018 61.12345645
22.49927265 50.97603094 20.78187489 8.56488513 43.91080281 17.81543432
78.7782316 25.66759763 52.38424086 37.02092364 18.8554492 73.5626346
3.11608418 29.0105353 39.20030718 99.50867062 13.53069204 63.80469653
90.48976394 61.90389222 57.08624466 21.64457633 19.79560735 39.94709462
57.71831654 6.62608098 22.11035348 78.28033116 60.29951023 82.72412191
1.97872723 68.04859944 35.19347878 38.41927052 3.4668523 32.6782931
47.21650552 75.61682339 71.66059917 36.27605229 52.83898831 66.94350591
14.12940968 38.5194144 54.83164276 69.63700918 26.46144227 19.58415156
82.92918693 1.71774771 30.44980923 69.97715967 10.18425337 64.5620373
86.88298015 29.00793124 89.2430392 94.10159051 16.2497822 75.24434003
70.78521065 96.47727536 25.9422232 84.10130591 24.45583698 44.74713656
52.37423926 26.38602457 4.44189628 74.91118164 95.37224811 62.19101748
37.06499326 76.73806694 10.12153442 16.04075642 27.46711386 33.0869005
22.57723467 21.85500319 1.35570883 14.06431437 66.10476198 28.78781384
52.07983696 60.85071332 82.68523429 45.56950227 93.85615111 21.57037397
26.12293567 33.78963247 76.07989431 64.88220676 49.62073908 88.34655394
36.82095715 80.32184855 78.70914902 1.61858472 79.98361459 27.36800613
89.1298073 79.80866899 76.87127023 39.80164067 10.3286838 46.66317808
15.41705602 53.75683295 76.37120422 31.52064983 62.49672242 48.62721308
34.0041175 82.57538561 75.21786018 16.47403906 48.35499641 71.44479364
23.15632381 25.45660717 94.9477546 95.46095269 43.42113614 15.09776957
38.96712226 36.15782369 88.85014149 17.47948363 77.48653355 26.38542418
55.6785427 68.28781351 66.38260535 4.71225575 20.36698345 47.46536825
31.46204776 63.9887434 81.11420024 25.26529535 61.91082568 34.41597742
48.25461649 32.07881249 29.2830838 15.09129334 71.64161084 83.46875217
35.18418687 95.54060465 99.03181425 23.76841577 32.63755174 62.72727161
41.92142241 50.73112969 42.98981373 65.10604923 61.98035584 18.20266098
35.34189251 33.33198582 42.47107123 9.88421768 44.15008186 54.07794724
65.58610245 55.90673281 56.0885261 97.60863741 93.94000363 33.80809703
51.61383493 22.56283807 31.2609811 45.29034721 42.3864916 66.63884959
85.06074065 4.72036859 90.10106087 7.85705246 15.46029347 7.13438245
39.64534777 8.39906334 64.62765086 25.94626365 57.39690866 38.8437682
60.39030533 31.4508706 64.69288693 83.56049715 40.74950402 68.78967042
19.81671759 22.14425949 62.55663083 42.38739546 75.61622047 83.10248805
61.43501567 49.76635377 60.10652205 86.86279341 80.23254515 56.68947171
37.97999422 65.59607046 42.44430906 62.4470033 8.39076318 39.17655498
29.00458085 79.44106292 19.43545639 55.99395283 70.46011644 42.89699409
4.51436389 99.15260109 76.47852186 95.23347307 18.75823218 58.15553142
72.8211056 8.14412636 35.60725094 91.38196607 14.79051922 64.01601457
98.43783333 18.19286556 3.4488368 85.85517698 91.75976794 86.13033743
47.91261913 54.21200313 55.69893785 71.34743866 51.23719879 14.34061522
36.48894921 26.14943114 84.21035056 18.31756924 11.07703597 74.72387155
97.53232941 49.83388029 76.7116364 96.61029568 37.19183661 21.60629933
9.68395133 28.2591939 87.73247918 96.48199849 74.33199902 93.63534994
79.16614098 49.26890301 80.27498948 92.10248812 83.24880899 54.96759173
30.45212041 61.6493061 64.97594514 13.29468085 63.47079445 26.34901243
7.10984835 99.42651214 14.44491001 37.01549057 4.80379012 76.81313756
96.3907321 8.60638385 22.36929155 55.70271319 54.93917771 44.0706408
95.48203605 8.2386028 45.52057718 9.33073277 24.71627688 44.6005602
54.43175662 63.91270032 79.90331743 97.51023081 71.89490558 31.90085821
33.42157696 62.16065744 37.28039304 56.44061719 11.76091543 66.30240238
54.69006054 81.40678596 89.71750199 7.99518872 58.52236595 19.79141567
57.00579983 87.21052812 96.18473949 92.42974994 79.63788795 6.76531561
47.74090111 68.04958458 36.62165503 61.44804669 89.24545999 92.74414604
29.44359519 47.58178486 30.12335391 34.66471755 18.64121741 12.16780453
25.53115248 20.782895 9.05462029 12.8691416 26.58767695 46.54270885
72.31202743 76.86195481 19.62701178 99.23910039 64.6914423 3.91430158
60.43677452 65.40009425 4.04010491 4.38120101 23.16501091 91.38876255
93.29301729 38.5613524 90.81575923 14.20561676 90.43468434 61.36768767
69.05122379 95.7384549 84.95653757 70.57699853 31.87103748 12.14990442
59.11527498 39.43487591 61.85096024 95.80999265 89.89120153 13.86641806
36.66523583 18.5260797 72.01201066 6.58981508 84.41156177 95.77455903
2.47116405 5.60246004 96.29874359 78.85698274 78.91069864 96.15272317
89.14917295 75.93308563 29.59044776 52.75282396 3.80869458 92.32711599
97.80813041 44.52763573 55.09379527 23.19496291 42.20873162 39.64461005
50.04790598 66.13948065 6.39093535 80.77135983 54.76937755 47.89899507
73.0929218 11.54446671 20.23757421 75.13130755 13.66088389 60.40694133
77.25529172 28.9753039 5.9083098 6.71561876 62.04464553 37.73585695
60.28047216 1.4419879 97.84291163 15.60269303 20.20820622 46.02766719
23.76551661 57.22599427 98.5517171 46.2786193 80.21760577 48.08466609
66.28164996 53.09277246 88.1146977 9.41089852 14.25656148 30.67136754
19.89709843 20.08454919 70.01839463 76.38956127 78.29997786 20.54638356
54.58521215 36.08866873 36.18107298 92.37174234 15.72907896 7.648907
49.47937061 84.17607119 87.72873274 37.65512653 8.36513945 11.03069455
64.92053836 96.74922719 30.78401691 12.57204688 29.51149971 97.37357171
44.72444392 39.69059056 67.20118389 5.3313384 48.40957943 82.91316339
69.03744504 30.04885969 99.90372027 13.11486354 57.99537578 48.09373644
99.4485018 46.56277571 41.13533256 27.53346885 80.94650988 94.61923237
62.12357519 95.24562081 81.87177476 4.47371603 80.70566217 58.56603333
28.85261147 28.06171654 91.33191806 96.09574939 49.43159299 71.21016547
81.8068996 77.10009862 5.82150473 31.99539655 46.33504646 64.960803
27.86624864 78.20590485 93.78382689 27.99254548 30.8575424 28.11722453
5.19636622 16.29426273 71.81170605 36.64171668 19.68771726 93.95533139
39.18377645 41.39561814 78.06777193 46.68031595 7.24888245 34.21721832
32.56677038 24.26705574 17.8626028 37.29776308 8.42512119 16.6483988
75.3575971 17.31976139 35.39371731 41.91133946 99.91459335 90.19138918
21.29736129 77.5224976 86.34412403 96.1160519 50.57393516 79.81717332
6.51879969 91.36071907 72.09100592 3.23169949 78.71775986 1.88881259
97.99063083 59.23264484 75.47792019 76.52010255 37.85928923 66.03385843
2.69713009 85.92588672 3.04187394 67.75055454 93.2072807 32.5749795
1.47652605 92.81027957 15.37079981 85.60581909 69.40960683 3.14171853
90.08512242 26.68199834 93.6726908 71.0490051 64.2118089 75.05241252
34.82344833 47.91056339 73.97294983 53.17348991 54.47586108 7.99964966
67.76711119 54.39270509 94.19472039 19.95092791 31.00546859 70.30724627
93.76005101 82.19935792 17.46876739 58.04262115 71.15448309 25.75663697
74.23738546 41.2632457 13.67042796 24.68555618 34.83794552 31.98730872
39.81978243 15.81144512 56.04972038 49.87381999 25.16367336 21.8974708
64.54419912 44.34335693 50.83352116 42.66720461 64.07761545 10.79486635
61.70290819 61.09843761 41.78431104 64.56928649 17.77737368 53.4394237
63.80718393 36.84018681 56.258088 12.07428847 33.84943776 62.27498568
13.22009408 61.19150509 32.42698616 17.62184982 22.09856774 52.65615432
48.5629697 1.47965749 28.00067248 75.03021625 57.07143559 43.54883628
87.13451024 40.5872974 8.28550278 46.38217048 85.10019916 2.2496047
54.4493561 24.56636594 71.52002151 37.27053938 98.6010055 52.25990381
8.68057003 45.09945123 3.77033596 87.11826532 95.77431849 62.87013442
97.73897506 72.39014598 92.22323908 35.81015146 51.25817631 8.56888029
71.78310681 5.10376465 23.16162887 28.4883719 79.366557 6.18144281
3.52354362 93.33421022 46.89648869 83.46048174 6.84391559 88.39576968
57.8285424 15.43193793 57.39934828 78.86747835 20.92846326 25.9287851
35.64327516 32.74828132 35.60505561 79.19855215 88.64315569 34.77932425
13.31988156 93.39047774 35.68241182 20.74848217 54.55534989 87.15777508
71.05904526 71.00502096 14.78060752 29.75642205 98.22048788 17.12547711
66.37295772 22.10546066 46.78596957 59.20653169 16.51837699 55.21003378
50.66674502 99.78869575 31.38138408 10.34390155 34.94572418 52.01626347
40.77933758 45.02577003 86.59797082 88.78105042 80.59808932 21.83785213
73.52692188 43.04511292 76.71127213 9.10291646 70.06294132 43.8415057
80.6212775 88.4738207 88.15157461 45.54065317 18.51304548 57.53275514
50.47951846 49.18405444 49.19939535 77.30799896 48.46882533 7.36317014
7.44123697 75.2350862 84.14249147 58.83140996 73.61111445 87.50138716
95.84526126 18.95700838 47.50841826 98.33085499 23.81170698 68.50756191
14.20087752 60.71381069 34.86587353 4.7298978 7.60625251 28.51777622
31.35123336 35.45866829 66.34471083 5.08836145 7.81515176 53.37662127
29.04271756 26.81981985 30.58241113 72.64774221 28.8591376 75.55124989
57.14136614 59.69083294 66.43438216 34.84620102 95.97003669 68.65439196
23.39880835 2.25193607 58.39411205 2.37448103 3.96890777 59.95180568
55.44819602 58.73517677 22.40521439 99.65780894 28.75140715 33.51451108
96.34897103 68.80268938 69.84015383 47.55457564 75.04989318 15.2285148
4.9371277 95.7052593 11.20228149 11.02122203 39.52731482 65.79950544
13.0861789 6.5939474 75.69693106 55.77672862 12.88202653 25.58028457
20.28535255 1.92753467 97.73725052 80.27791495 62.85534788 6.69571918
26.98421898 16.52448181 60.70763527 41.71452447 84.41001738 20.12519424
68.62613246 18.63266488 65.9955708 75.81531823 4.03964042 79.08304851
64.46012264 2.18278002 92.7209911 2.58420085 38.85230458 66.71454761
23.30870727 28.2717718 83.64822772 67.23600585 99.90357523 86.1520731
96.63795882 41.16851603 85.66577608 81.77574032 49.42122337 24.03400349
11.36131284 94.64276696 89.36680683 86.61351433 97.77763024 51.09711967
54.07726466 87.48431666 45.83131831 68.12958803 22.73510458 42.53784784
21.36956721 60.04558562 92.55399448 11.16297495 4.47767896 55.13193112
21.31705044 12.96491349 69.50056295 55.66050524 85.7032385 75.05603818
75.5486248 42.50764961 52.13324516 26.17736985 18.96337422 44.09868694
49.29222618 38.31933985 68.34953246 33.08309481 12.83162325 56.09152106
78.74034117 70.10454964 83.34618724 74.61596766 80.18059938 98.86983752
93.07990582 44.91476473 26.90071107 61.56405521 74.92335212 93.22947626
28.94834503 94.1836538 20.26878014 27.97633757 64.78851996 96.5991357
44.81262344 55.38504836 65.45273326 26.37152541 97.7218574 90.85703774
52.66162428 5.64060001 98.29908687 76.84794988 85.78134082 47.44060203
86.44076967 95.24120458 21.0463304 52.15380461 2.9478808 64.23191127
60.90946438 55.63561004 14.80650409 65.57481773 35.74064608 78.21188551
99.07690414 79.52796464 69.44980614 94.78135049 96.54595203 41.35734574
43.87590853 44.49771476 56.42349144 9.52677106 94.40228687 71.79701483
32.90725852 68.34136356 8.63937706 58.70934791]
# 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 = 10)
plt.show()
[49.78437725 51.99427338 60.18856956 47.45922247 48.66476527 49.39656669
56.47246086 48.20124236 53.83818719 45.17552798 46.08305192 46.21827695
50.55429304 50.29638955 49.49455302 53.07502864 52.65535633 52.93576361
45.87435177 45.52072163 55.1997337 60.3360522 53.25659636 49.20896946
48.89898666 59.92581216 58.42413857 55.87420708 53.85194353 48.23140061
51.98471766 60.75236715 38.97590303 48.24464462 46.40284401 45.75075279
58.07752984 47.5106838 62.73294221 49.08192762 44.4989353 53.74144584
47.49099832 48.79832561 50.64202145 55.94660578 45.59519596 48.99840534
42.97900558 53.95098392 53.50339997 51.62090543 43.67181826 46.77919834
57.2343127 48.40337913 49.70413628 55.34996594 54.23168033 56.07401396
42.39124408 52.58716099 54.24229242 55.46570848 53.57753491 51.94849096
52.9247863 38.13030169 49.20947184 44.00258909 50.17069462 44.58040588
47.74399453 44.9246653 52.86526789 53.4095422 43.74684954 52.42472519
51.48253196 52.59821032 46.46781658 44.4465532 49.90772041 51.60292082
56.81952951 39.73482139 45.57221098 56.39493154 52.90826765 51.26686627
50.03910037 48.52770451 44.29230045 41.34227707 62.64594147 52.55941366
51.45637775 54.99485758 51.01245298 52.09350324 57.03565349 46.42081064
41.68760894 56.75077421 46.63750371 53.65581835 50.34721175 55.95152353
53.20088718 50.86984328 46.09096156 49.43772703 42.03144685 50.58755013
59.91477103 51.46969955 44.32954818 51.4444517 53.43519889 44.09059653
49.59026676 49.50523787 44.58413838 50.21843859 42.48115425 48.10112466
48.14554859 50.26874825 58.46142954 42.31169485 47.36524832 43.6890525
52.89192947 43.46741754 51.63769393 51.70533803 58.34095255 51.71883813
45.26369986 48.65931397 37.78406491 52.64282253 42.31609751 47.44847404
52.29181397 62.41520181 51.78359971 52.87034994 46.02680609 55.57346584
45.55131756 52.72149165 53.72834537 51.25904139 43.6872425 52.03151617
51.53446613 43.74724436 47.13210268 47.87883275 52.58629726 42.5127564
49.378254 52.00447953 45.7201301 53.72116203 50.36650771 52.83088557
53.02607635 45.02824748 49.89067032 48.96896676 54.34898505 52.73838449
58.34450402 45.35286453 52.16072641 56.93038692 43.54254657 48.5553002
46.74971433 45.99580054 56.88020179 55.94749293 45.27569548 52.57943958
55.82183582 50.61454795 46.0132672 55.43269987 46.66329212 46.27275339
38.76726486 48.79553756 59.0842709 43.7156399 49.1294579 46.85880266
43.32861952 37.56998913 47.30117276 51.33095432 55.48572891 39.70860394
50.11680314 54.92438757 47.6328606 42.54766353 48.84890102 51.85968856
53.97996712 42.6252524 49.68310225 52.29343798 47.16357484 46.08939061
53.44797143 54.49275436 53.02221486 47.66810959 50.01034055 42.61913696
53.2649894 49.0786202 52.27043482 53.61191887 48.92140371 48.47970226
56.73481818 52.90745773 49.34297643 49.32483315 52.87518814 51.17155072
49.91531001 44.07395633 55.92240074 55.36832953 52.30412478 47.29378646
56.18999567 52.08969259 52.01794492 49.27322276 57.32453062 43.35036226
47.78904463 44.32722282 52.06131264 48.00115949 41.39738016 48.53186022
52.69591935 53.97681401 55.68150561 45.20164194 53.68823409 47.33148968
54.36937614 55.42831804 53.10481755 47.89409398 44.78342887 45.93343503
50.26173981 47.19374383 53.63181569 46.99406976 48.62518598 53.5531508
46.79996874 39.46748757 56.55058545 54.22874371 47.91942328 44.84619239
48.16526508 50.41424461 46.18682459 45.38866372 43.82731358 46.81313728
53.2795191 51.37011798 39.64423247 43.59238801 50.67277754 46.14400984
49.74892518 46.17441282 46.68979176 48.91118253 46.1838841 46.78605232
43.92494084 58.44786008 55.20512077 52.48966444 51.9951801 46.43789316
43.10576752 50.91707747 50.67780344 57.46327287 40.79799916 50.65055004
48.96399648 47.39622351 53.19649528 55.69764203 41.54652115 39.10932707
53.62943719 44.40202696 40.35708126 54.66317871 41.76049333 56.81486302
49.98214529 42.68194812 40.09293702 51.23416529 54.21272961 40.92635727
51.52059406 57.91177406 56.80810257 50.0517613 55.0317973 50.2240756
44.97472151 43.6913889 50.74780475 54.62306 42.23491065 49.99088018
46.89813629 59.14064761 43.60761867 47.63872506 59.36532101 49.86233436
48.92764935 59.13807972 53.47301974 60.00783508 47.23460776 46.31156761
48.52335379 49.83455923 42.5480424 42.65031892 48.23950824 47.00440954
43.29990047 56.13334897 43.85863479 53.86642646 53.24691163 45.83424163
43.76190342 45.78091455 54.83518305 46.2099115 46.70569012 61.07463932
45.96669844 44.3799269 47.90171462 47.47725838 50.82896379 42.13658376
46.17286924 47.92837817 42.53408751 42.80228403 44.2832788 58.66956132
64.86814683 52.76424152 49.89905517 54.63849709 52.86947067 51.07714059
39.03109889 43.61456982 44.35118688 50.10990651 54.79388258 46.77549775
49.71927297 44.38261193 49.78277057 50.96345682 54.64583194 50.93930349
55.54886845 51.10401547 61.61343863 56.36248583 51.21468486 49.40061956
50.60133485 51.03665717 49.09214717 47.22839529 43.30569096 48.96847314
57.01803004 37.90084015 55.20217827 55.37227912 48.52417536 52.40786528
48.36088971 39.76634274 42.26906963 48.61598775 50.50936583 50.81055619
55.61552002 46.34717932 41.75985581 40.7651094 45.80587373 58.0291214
55.19563959 52.50546298 50.17127882 41.76112984 53.51655455 47.2082698
61.27683201 58.92331864 58.08870523 60.31205869 48.05966233 50.70072543
49.60437093 39.44970132 50.93746154 56.19208431 44.79155928 53.48510889
44.81566523 49.09080255 48.25557459 53.1689974 46.15923569 49.0199587
39.05663199 56.92148327 61.20567518 58.80286144 56.42740744 50.79996174
45.70295308 51.39461468 57.80124593 43.10788101 53.99469519 49.10088582
49.44071704 44.89293184 59.6383335 50.31233929 46.83010699 62.61333026
41.38827166 48.50991763 51.26541916 49.3037504 56.76734096 48.33210495
51.52234391 51.04016015 45.9242699 58.45175405 53.51533356 56.99945062
42.96647884 49.44893061 57.39573675 39.03934869 49.02944464 50.27394408
43.20962112 50.5504319 45.58079573 51.45337168 49.7421136 55.18937922
45.05636668 51.42943138 46.87948173 56.0601339 53.01520212 52.04803512
52.77272397 47.66935659 53.49710264 55.3068801 44.29876002 50.5211681
56.06992088 50.69411999 46.89651963 54.61619178 58.03961749 44.18680731
50.23774102 50.85809569 56.93989501 56.85722826 41.24002805 43.12596019
50.72623591 51.12146442 50.16475649 57.60033366 52.00067406 50.45430167
55.75652657 53.94350083 45.01884488 56.13005012 52.18089086 58.19827424
54.05629317 54.45747461 51.89705692 45.35487309 41.44389591 44.73854761
49.6745033 53.15922798 52.19894262 45.84453684 51.10177713 51.56574361
48.43387315 47.51104514 58.97539083 55.45841563 40.98623644 49.09103545
46.42316918 44.39879667 48.86639017 48.31162514 58.66754544 46.53427323
47.11245595 47.68300377 54.05979108 56.66574883 57.73387321 50.77784142
57.45235071 54.12186589 49.38083031 52.90357642 47.78317358 50.92154456
61.05118784 55.22126359 43.67337466 56.01339687 53.02773939 44.15118822
54.26211472 46.1157691 39.53884535 43.30452242 49.39683524 54.27519346
50.58992825 49.81499071 57.97914872 55.52275223 42.9919717 42.05030067
45.47081972 55.15877993 44.50975788 50.43523224 55.90986198 51.50860595
55.77745556 50.36803623 46.25062486 46.06711692 52.0872308 53.77089528
48.54288784 56.78573098 40.77972986 47.48358466 53.31191441 43.10048567
54.6422091 56.00024674 59.54569289 48.91196527 46.8978924 47.95311976
52.99588867 44.07636241 47.9207992 55.45353915 57.68120226 53.69983409
46.35458137 45.42167768 50.09597548 44.16894218 54.35381273 38.35396225
53.89830223 39.33755943 50.54246659 60.36151348 50.5302237 45.80951567
50.88732422 49.90142439 44.19763793 46.15745491 45.4386396 49.48063122
54.68646407 48.12358805 48.03951403 51.28586045 51.01164613 48.6462311
50.36625665 45.75776064 44.46433686 50.96702653 52.43679165 42.17141332
51.20565225 38.37870946 51.56079432 58.58352408 49.4672286 56.35544701
48.63779557 41.57132822 53.94797122 46.16371885 50.85433196 53.65582512
51.13765287 52.80213216 56.48523547 45.60634437 43.98963541 48.54728778
46.46931077 58.75146995 49.60812455 51.17608422 52.95097683 58.96459899
48.88228082 47.7295716 48.51040337 46.3119123 50.34580442 46.15205138
48.36182559 52.5765285 47.70197044 57.57012968 42.04679181 45.26478529
50.96435138 53.13030259 57.28584733 49.92411463 46.47109598 49.24130933
51.09951646 44.69779155 49.96171307 47.65078125 47.06279393 44.80061214
44.13103505 52.88699442 47.29061745 57.60685501 57.14166227 60.55356128
46.04131646 48.54833806 51.6259804 55.52295818 45.75586389 51.77577268
51.67055116 49.37864232 47.18184544 43.59154991 59.38882544 54.60711972
44.39513601 51.78323664 48.13669631 44.72076511 52.27538403 57.33142995
41.57127613 52.25119507 48.6590361 54.7209152 51.02164432 51.56003308
50.42969111 42.48488604 51.90294927 51.87572864 45.1491786 44.67620468
55.20778733 44.10547936 58.49178868 55.72235972 44.99443313 43.04017605
46.87985871 53.55983734 53.60364074 54.47847796 47.32419854 58.25975955
40.63255579 47.08881404 52.74655542 54.16033443 46.92018552 53.38953221
47.14586529 50.71841882 47.77482472 50.30415859 53.48294741 42.8873013
41.75134207 57.18014801 49.1986318 51.02282351 52.61699776 48.22544806
53.72900532 52.84487097 49.64894103 54.78795557 51.09680678 55.56181225
52.92363358 46.63140828 50.82504647 42.91094932 47.18492041 47.98636591
53.84855396 59.94350307 47.63065676 51.0693363 45.99059993 50.05568559
42.20423945 52.26873114 41.29910445 46.02316693 39.76007896 46.53283092
53.31813657 50.76103934 51.03090021 51.59037239 56.51204266 34.41084234
57.27165815 50.4985833 43.21248897 47.19296264 60.87686557 44.65556608
46.59234646 39.15735016 55.87651165 54.05851998 46.0310173 57.47125509
50.49996338 54.60375141 50.15046548 49.63910159 51.69793386 51.81362614
43.37097548 61.68952207 57.72778166 44.91034789 47.62769298 60.92858642
54.87990809 50.65684938 48.09055797 55.06310255 45.37868455 50.65678902
46.65374322 55.90705887 51.16709176 51.94450157 49.03184917 48.34235137
51.05545723 54.83472195 52.32574507 53.68340851 47.61557473 53.2115597
48.26894055 48.40267549 52.88543508 56.29059762 47.45529269 47.81102711
54.37007717 51.87054967 57.833648 44.77521488 46.21749556 47.72301718
44.33375386 45.96235186 50.04341161 48.8886735 50.32625089 53.75816611
54.29521258 48.95225987 56.47301941 50.0401752 56.29221773 59.01644155
50.62244911 43.76913478 45.72709638 49.15093149 54.81963567 49.33327308
56.20836775 49.7620876 51.24480504 48.66101954 52.71254737 52.70134574
52.72069506 51.49231382 48.2596306 44.52754636 50.65031905 45.10912368
52.46071857 48.30359644 52.62708395 49.21211741 47.00722673 51.5767104
45.76274696 53.62613846 58.85151062 49.38391564 47.08876595 58.86947097
48.23597955 51.13565887 48.95361404 50.42664359 55.19518678 50.63661067
48.521409 46.16258669 41.90321909 46.39561152 49.85892542 54.03029461
54.63619259 47.45693339 51.66771907 43.40406537 46.05570204 52.95827013
53.68916232 48.92299899 48.10923686 56.53397018 53.05441085 51.05304497
47.39700712 50.13291839 51.84502354 54.12069794 42.37314268 53.47814588
42.83221253 49.81751947 48.83542665 44.77351363 51.75634699 51.29202446
53.31841761 40.32496553 49.33533084 47.61630105 53.67054643 54.28596571
54.20474783 41.80059955 54.61026852 50.74590577 46.84100562 48.29358673
47.00152693 39.94860821 48.89891849 51.77719674 52.31472401 56.34083684
41.08003736 49.78978044 47.10966368 56.92362947 53.39557675 53.87586298
45.77422011 50.57503484 44.60102599 45.91103685 55.66497788 59.9033748
51.61556711 56.3724954 46.96674575 50.22664473 64.98578998 45.61430946
44.71980303 36.54890238 55.10980632 48.6616732 50.21416396 49.80068801
51.64087272 50.28010489 54.32133146 43.0799799 51.79218904 49.42763316
52.26913011 61.52486261 48.74263564 56.56143241 52.85550921 45.81791678
49.46943005 53.52880517 48.1949664 55.60262164 46.22847085 45.75062276
48.40221932 45.93192112 51.41894979 47.00506939 53.57140409 59.14555154
48.97797466 51.69416573 47.90266473 50.31409071 51.17097637 43.58070637
50.63642096 58.46871966 41.73598877 43.06456758 44.96465203 49.92324409
45.32417653 47.72469774 52.26186587 51.95938986]
# 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 = 1000)
plt.show()
[48.08661287 39.07806357 41.94795362 53.27960089 49.6067504 45.92076338
45.87310684 54.97819536 41.77134341 50.46079882 43.07899786 48.82076498
59.64736433 45.90515584 42.06153482 47.55164282 46.71233352 47.41316706
51.32913629 43.38469464 48.73533948 47.07766855 49.57707077 57.81827488
57.90971541 46.81166011 46.8514688 54.46795109 50.60688158 48.37780901
47.54759277 37.84926104 50.48011473 44.24242453 50.92276743 54.01197869
49.97717801 57.09374862 48.07009246 47.96336538 48.58894845 44.64856864
56.65639032 39.435101 49.71418829 42.07835023 59.49893881 43.49513412
44.79342474 45.990202 58.94163345 54.40396892 45.3595283 51.81635525
46.4041593 54.45689975 46.20447705 55.18549741 47.17795709 44.69789189
50.37952325 52.37301607 49.48700246 57.4872804 45.76014945 42.25048337
40.86998238 49.75719014 58.84716165 51.31495959 59.11801953 47.0767233
51.45571029 55.19555392 59.93599547 45.39498997 51.90085949 42.25707955
53.27681519 50.8720637 52.4680137 47.38413542 60.82983301 40.08552256
48.97728036 47.27232177 52.01875989 55.62836494 46.59850073 46.5571856
50.3594895 50.42205911 45.3046883 48.73457577 48.6659413 57.54626642
50.21809231 52.17361218 46.52666948 55.83659917 50.60162247 40.07664198
52.22731649 42.68914549 47.57949961 55.51638016 49.48232263 36.76722732
49.17152809 42.2320395 50.13282195 48.88615748 51.45387 39.25641354
49.04936039 51.15256668 52.61428229 58.03403174 45.61018555 54.78060146
50.08174584 48.130498 46.0814803 52.16521963 39.09204124 52.45669163
50.28905227 41.87640234 44.78880721 53.78907811 44.00745801 51.87207428
51.13265362 50.01380275 51.31715143 45.21046276 53.47902855 43.26021909
50.09860356 42.6805422 49.91587166 45.31828603 45.00388723 46.14051338
55.14902684 52.64218782 45.72219035 50.21536862 55.00892378 53.08927313
54.34754319 59.47665374 42.18492569 45.36818441 54.9717421 52.40353645
54.03514647 47.76877138 42.13514364 45.13983845 58.29020762 59.09356574
49.78028104 48.55715201 45.1270735 47.19532606 39.09253032 55.31531723
54.18583087 46.16278715 48.6026875 45.69854844 45.67470157 37.33150503
44.04957305 55.62751235 52.57112774 45.79579179 43.7262826 42.50397533
53.79479728 63.7915214 38.8773223 49.56710315 55.8034176 54.44769928
46.80128028 47.99397562 53.36660611 45.81452567 51.19541916 49.3223426
60.97599614 37.36655451 42.38014256 47.22713979 51.67295641 52.30907983
42.75331308 42.85533731 45.44311185 52.98936095 43.00362132 54.13373147
48.89599379 42.9363316 53.12095498 52.2607584 49.40934549 53.18534924
46.89844578 50.0961784 56.30924408 51.06417479 52.65745182 51.1278187
51.54554529 43.04408398 56.95349287 53.67232766 52.61349324 43.92880337
45.40096282 43.65182046 47.46875143 42.84881077 43.41716364 40.78044949
45.20748433 48.11449145 51.59283085 47.33510293 47.755726 51.55880837
44.06825906 52.57424232 51.10068862 53.47076603 50.39042177 43.57735684
47.89756647 47.50910278 55.58540186 46.57202182 53.50479275 55.17280445
48.16624311 48.44180738 49.94315256 51.22429279 44.06652799 55.10020762
58.22080241 56.4126915 51.18949834 48.26269972 46.8028979 47.60550055
52.60683088 47.39009222 46.92591537 59.99240236 51.3682467 39.31653867
39.98654395 44.95445672 53.35496936 57.90810367 57.66446923 45.27075756
41.96215457 47.57324245 44.04565451 45.78734078 55.15713401 53.81885424
53.83906286 43.27839364 46.05746365 45.97839055 49.69703231 38.73250161
43.04509337 49.84323368 53.93679577 55.2607108 50.8377459 46.020194
48.01294919 49.18939563 49.76656758 50.50482222 41.37054513 40.52175772
53.24009859 53.27230546 52.14209749 49.59568426 50.90513367 51.97462484
43.0779372 49.16922552 55.62756763 49.34083253 44.31104216 49.09718777
55.29009191 59.40613532 54.99502209 52.81461308 46.5863579 38.05780446
50.01612373 50.43509891 38.94453565 46.3943191 54.02928138 47.2659301
47.88037689 50.5332732 51.25348236 40.86466693 54.15324875 44.52632218
42.28797278 42.53453285 50.40700403 53.33306892 48.85559522 53.18446315
50.94437197 54.11774665 49.85972126 54.7272534 43.77949965 58.90239003
46.57441452 57.87979344 54.41405398 42.14183806 54.47158833 49.56288086
52.39995713 45.81533665 50.60116703 55.75819498 44.60795585 54.15471998
44.90992943 49.73399337 47.16807979 51.71338383 43.8288988 56.76516213
52.27760143 54.30993162 53.71802365 48.56632888 52.3831759 55.74378081
50.5431836 43.68604787 50.38938625 53.65769206 53.76209486 53.34701313
48.54095781 47.00941605 48.3762384 56.7028904 53.11465327 49.48074623
49.91293741 46.0617582 48.95554201 51.75939594 49.26147955 53.34093294
48.51616812 43.11264914 47.3705811 49.9986603 42.62959591 44.90537303
40.93882423 42.34231778 50.03659848 53.25063353 48.7230571 58.06679828
50.73617822 56.79058627 50.25266323 46.96053428 45.9797394 46.88510913
51.75650682 44.17418651 47.8432903 48.53290958 43.56383322 49.83957782
55.85928876 50.37139227 48.4946643 47.54813167 47.54722781 54.75911776
49.37845871 40.0798582 44.79039699 48.92697417 34.50991881 48.73766312
54.90709621 54.51219559 53.05026709 46.83347633 46.9961813 42.23348884
56.08979445 55.14963455 51.72875562 53.94302536 53.41577589 55.73750508
53.09536866 51.42829207 55.81953445 49.91044648 47.12640091 44.74259242
53.93567154 50.52904151 46.6829532 48.32067967 53.68758521 46.42162449
42.65113866 60.10365079 49.65492194 53.03758045 46.70734792 54.15462711
55.58907996 57.19848242 42.00754644 40.95480351 58.73321621 49.61136666
42.09021462 44.53529484 56.03553853 51.57423189 39.72239495 47.20166539
49.70198854 49.11800359 45.18924347 48.13690306 53.28697043 41.76086344
48.47046885 50.276374 54.34471878 50.72530007 50.81875918 53.18589355
48.43254931 50.67950345 43.32359761 54.82298242 41.76795145 51.6809307
47.13125601 45.3783919 56.32598088 54.86186071 41.90433761 52.43955128
53.28186492 53.77719392 54.55560891 57.78493919 43.79295206 53.04712212
52.70135776 57.29709407 51.59634196 50.57954943 61.96352312 58.16491681
55.42364489 52.41920826 49.69261031 48.11427587 53.6464654 47.27191639
49.47301841 49.24259755 60.88671641 44.55097497 53.0940107 39.75516495
48.9927966 53.75947582 50.16139695 45.6476244 43.81689342 53.65332047
58.88817074 55.0495749 52.92417904 44.67793971 53.14335619 53.11619474
37.54237918 48.72488865 44.38687665 52.63927429 52.33270428 50.72004989
49.74692056 51.58633695 49.6322946 45.72026811 49.94889549 55.29329813
46.66761253 50.57242254 52.12818087 55.9449623 48.38616581 53.03038287
49.27945988 48.58837922 58.53569841 57.44864924 50.57424738 44.09943886
50.32912854 52.80625086 51.28094786 49.08893221 57.78286112 48.83715588
45.40949978 42.91226157 45.24600099 51.38504337 48.24539802 45.98851278
49.75854246 51.31852274 48.71478753 49.2953556 53.36042306 48.30509248
44.18811787 45.70804743 45.57113558 50.29386864 53.31354322 42.30216079
61.5858653 47.38480073 48.3740197 56.3659595 52.09992398 51.27797886
48.43438626 42.15532217 47.1975179 49.02015288 44.62301097 54.9495263
50.61905096 55.19435021 43.09730036 62.69852047 58.81592375 47.49806206
53.54863653 53.67309767 43.699315 53.29799824 46.23406046 47.96513185
48.7865128 58.31854952 42.17887673 54.00603962 53.09173362 49.9928429
39.11447689 52.12694122 52.61075887 42.82634529 55.96511618 47.60848843
46.07075516 42.91118682 40.65803534 51.61958737 36.57441267 45.98185579
52.69109476 53.24404944 47.98093854 46.03499412 52.16253434 50.70935181
49.28925318 61.39598813 46.55038198 53.11960578 57.12126258 42.47020128
50.14166355 48.63691767 57.91645081 47.04675719 55.77691385 46.22577471
55.92297268 45.43341804 47.82901893 51.10959797 59.18262653 51.78921812
43.22953458 59.06829399 56.37545782 59.60357238 48.41428249 56.81789917
50.53380852 49.95153867 54.31111305 49.3926305 48.06206297 44.76479877
48.1274256 57.95698078 56.92166208 51.97240241 50.14261208 49.22593638
48.22204222 47.78274674 47.32932122 58.43714083 49.02087686 51.44846327
55.41363528 49.11560523 49.880955 52.46107866 41.42536546 57.31622075
59.88348279 52.02303694 47.8013688 53.16079007 41.72079586 49.54431045
49.56533735 44.3030963 54.30093249 52.02139326 43.78756582 49.85500817
49.84507328 52.92865861 56.56361824 54.2574908 56.61394435 49.79882445
59.4001131 52.33352607 47.11272221 46.55109314 46.74646263 43.9242481
45.8970357 49.19399694 50.24770225 52.95197678 48.06695444 51.53772859
48.06084646 59.62126032 47.41015287 50.98803184 51.41337398 50.51622229
53.83583764 57.02806457 54.32938153 51.84908049 43.031956 44.19511095
50.10883128 36.25812921 47.11829834 43.49977918 51.05434391 48.93767775
52.02485815 42.67607594 43.02680516 47.18812984 35.61597981 41.53780879
55.98003759 52.53535276 49.51198966 48.51219885 44.77943458 53.18872074
49.57662058 57.71423969 57.48497153 45.46194873 52.39218399 47.46181805
54.06454354 54.19093315 53.31526567 49.189246 43.07101509 50.40204701
49.2864502 43.91629122 47.70702963 48.13594475 48.72913345 58.93039143
51.03529958 52.92037154 46.88741575 58.92612985 47.20371246 54.82810911
54.25367369 48.10319978 54.68577738 57.1995141 48.76257761 55.63299614
48.65143009 57.60359549 42.29705102 59.13764801 56.98843253 42.9367375
40.6922709 46.0752003 53.73384257 51.28290072 59.77374782 49.21285373
47.2456088 51.25899697 44.23708146 46.75612772 55.2255215 47.01041872
48.28799637 54.48774027 51.92572719 51.07903169 52.34313224 49.36394815
50.74987564 46.10570902 52.14790427 56.26767912 54.16227462 50.16493448
47.17199244 50.76312388 56.87488457 47.28104105 52.44383977 39.85826998
47.42107407 47.58416856 54.04050986 48.448665 58.78170417 56.54436387
48.25556135 46.15049362 42.00128528 38.64337522 53.29362009 52.73938191
55.88880964 53.86330718 44.14086835 51.36743802 45.27390606 60.60265851
55.16460944 43.09459713 50.56678937 48.93299622 51.95523669 56.04414529
45.29880963 45.98953877 50.14113047 44.14663165 50.32580781 53.26335128
52.06498285 45.43761221 50.84997681 50.25531711 50.04366969 56.91892954
46.65938008 42.4106117 51.48063862 43.33145919 47.10002679 48.86433687
55.25921178 45.7777985 52.89235298 47.83848651 48.49214166 45.7355749
42.76522171 51.84244592 60.69886093 45.69452672 49.45682991 54.10304246
44.8220148 46.47129941 62.72009482 45.52838229 45.71227129 49.82161264
52.64299667 52.14355947 41.43856229 49.81073956 43.31010094 49.4599718
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59.56474249 52.24610174 65.01268579 54.78025768 46.43064298 50.40410288
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50.86612423 51.5443088 49.97426534 48.55423137 53.03007424 44.17272882
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53.76437869 56.89925384 50.71060955 49.9697066 53.91067418 49.91149502
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47.99025972 43.43522092 50.1607805 47.35175574 39.61989731 52.11571148
45.74817211 59.11771476 59.96054185 50.52712412 56.96312127 46.13123195
46.58590779 48.19275606 47.02469433 45.12910752 50.05011048 54.92650537
53.5458107 47.39752217 45.43063078 43.4196969 46.79896926 34.174929
54.19170594 53.4950066 45.53164166 54.12584049 53.25226746 46.47253898
46.27932143 56.68039224 43.30436113 42.71386752 48.66153169 59.71677282
36.41139811 53.69652556 49.89220168 46.4220644 46.1850975 49.65294717
46.81181831 55.05667204 41.99526394 51.35956553 52.63939179 47.01600674
48.48708955 49.26822921 55.16166752 54.08054399 51.07190715 49.29065489
48.96816407 52.66953598 48.7153742 55.7682499 46.15674571 45.62197315
51.24731922 58.9635729 47.15697814 44.64412602 47.90356141 50.7751073
41.84340626 53.17204613 53.37840048 49.72322384 52.21465963 45.03372397
49.2955803 57.22980407 48.94046015 49.64300829]
# import random and set seed
s = np.random.seed(1234567)
# Simulate drawing a single ball; each ball has a number from from 1 to 50
x = np.random.randint(low = 1, high = 50)
# 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)
a = 25
b = 0
for i in x:
if i < a:
b = b + 1
print (f"Balls less than 25 are: {b}")
Balls less than 25 are: 50
# Calculate discrete probability that you will draw a ball with a number <25 using 10,000
# simulations
x = np.random.randint (low = 1, high = 50, size 10000)
a = 25
b = 50
for i in x:
if i < b:
print ()
Execution error
SyntaxError: invalid syntax (<ipython-input-20-cca4ee285356>, line 3)
# 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
def ball():
x = np.random.randint (low = 1, high = 50)
if x < 25:
print ("true")
elif x >= 56:
print ("false")
print (x)
ball ()
true
13