# import the library numpy as np # import the library matplotlib.pyplot as plt import numpy as np 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 with 5 bars x=np.random.randint(low = 1, high = 50, size = 50) print(x) plt.hist(x, 5) #5 is the amount of bars/bins

# generate 10,000 random integers from 1 to 50 using random.randint() and make a # frequency histogram with 5 bars # compare with previous histogram y=np.random.randint(low = 1, high = 50, size = 10000) print(y) plt.hist(y, 5) #5 is the amount of bars/bins

#compare previous 2 histograms against each other with 5 bins plt.hist([x, y], bins=5, color=['red', 'blue'], label=['x', 'y']) plt.legend()

# generate 1000 floating point numbers uniformly distributed from 1 to 100 and make a # frequency histogram with 5 bars x = np.random.uniform(size = 1000) x = 1 + 99*x print(x) plt.hist(x,5)

# generate 1000 floating point numbers normally distributed about a mean of 50 # with a standard deviation of 5 and make a frequency histogram with 5 bars z = np.random.normal(size = 1000, loc = 50, scale = 5) plt.hist(z, 5)

# generate 1000 floating point numbers normally distributed about a mean of 50 # with a standard deviation of 5 and make a density histogram with 5 bars; compare with frequency # histogram # basically just copy the formula from previous question but add in density = True parameter! w = np.random.normal(size = 1000, loc = 50, scale = 5) plt.hist(w, 5, density = True)

# Compare the histograms from the previous 2 questions here! # z = the normal histogram, w = the density histogram plt.hist([z, w], bins=5, color=['red', 'blue'], label=['z', 'w']) plt.legend()

# import random and set seed import random random.seed(1234)

# Simulate drawing a single ball; each ball has a number from from 1 to 50 random.randint(1,50)

# Simulate drawing 100 balls and keep track of the number of balls # that have a number less than 25 x = random.randint(1, 50) n = 100 # Number of balls being drawn less_list = [] # Leave open so it can be filled as the simulation goes for i in range (0, n): x = random.randint(1, 50) if x < 25: less_list.append(random.randint(1,50)) print("Less_list =",less_list) print(f"Out of {n} simulations, {len(less_list)} random numbers were less than 25") #len(less_list) gives the number of items in the list

# Calculate discrete probability that you will draw a ball with a number <25 using 10,000 # simulations # Discrete probability (D) = chances of the number of balls being <25 / the total number of balls # Basically copy the basics from the last problem but change the necessary values y = random.randint(1, 50) n = 10000 # Number of balls being drawn less_list = [] # Leave open so it can be filled as the simulation goes for i in range (0, n): y = random.randint(1, 50) if y < 25: less_list.append(random.randint(1,50)) D = (len(less_list)) # The number of balls with a value <25 print("D =", D) print("D/n =", D/n) print(f"The discrete probability that you will draw a ball with a number <25 out of {n} simulations is {D/n}")

# 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 for i in range (0, n): pull = random.randint(1, 50) if (pull < 25): print("True, <25, win!") else: print("False, >=25, lose")