# 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
seed = np.random.seed(12345)

# 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)
plt.hist(x)

# 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)
plt.hist(x,5)

# generate 1000 floating point numbers uniformly distributed from 1 to 100 and make a
# frequency histogram
x = np.random.uniform(size = 1000)
x = 1 + (100-1)*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
#
x = np.random.normal(size = 1000)
x = 50 + 5*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 density histogram; compare with frequency
# histogram
x = np.random.normal(loc = 50,scale = 5, size = 1000)
plt.hist(x,5,density = True)

# import random and set seed
import random
random.seed(12345)

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

```
27
```

# Simulate drawing 100 balls and keep track of the number of balls
# that have a number less than 25
counter = 0
for i in range(100):
x = random.randint(1,50)
if(x < 25):
counter += 1
print("Number of balls less than 25: ", counter)

```
Number of balls less than 25: 54
```

# Calculate discrete probability that you will draw a ball with a number <25 using 10,000
# simulations
counter = 0
for i in range(100):
x = random.randint(1,50)
if(x < 25):
counter += 1
print(f"Probability of getting less than 25 {counter/100} vs theoretical {24/50}")

```
Probability of getting less than 25 0.49 vs theoretical 0.48
```

# 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 drawball():
x = random.randint(1,50)
if (x < 25):
print(f"You win! with number: {x}")
return True
else:
print(f"You lose! with number: {x}")
return False
drawball()

```
You lose! with number: 43
```