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Introduction to Probability Distributions
Random Variables

A random variable is, in its simplest form, a function. In probability, we often use random variables to represent random events. For example, we could use a random variable to represent the outcome of a die roll: any number between one and six.

Random variables must be numeric, meaning they always take on a number rather than a characteristic or quality. If we want to use a random variable to represent an event with non-numeric outcomes, we can choose numbers to represent those outcomes. For example, we could represent a coin flip as a random variable by assigning “heads” a value of 1 and “tails” a value of 0.

In this lesson, we will use random.choice(a, size = size, replace = True/False) from the numpy library to simulate random variables in python. In this method:

• a is a list or other object that has values we are sampling from
• size is a number that represents how many values to choose
• replace can be equal to True or False, and determines whether we keep a value in a after drawing it (replace = True) or remove it from the pool (replace = False).

The following code simulates the outcome of rolling a fair die twice using np.random.choice():

.gamut-6x0oro-ColorizedContainer{display:block;text-align:left;font-weight:normal;background-color:#211E2F;color:#939598;font-family:Monaco,Menlo,"Ubuntu Mono","Droid Sans Mono",Consolas,monospace;font-size:0.875rem;padding:1rem;overflow-wrap:break-word;white-space:pre-wrap;-webkit-font-smoothing:antialiased;-moz-osx-font-smoothing:grayscale;}import numpy as np

# 7 is not included in the range function
die_6 = range(1, 7)

rolls = np.random.choice(die_6, size = 2, replace = True)

print(rolls)

Output:

# [2, 5]

### Instructions

1.

Run the given as is code to simulate rolling a die five times.

2.

Change the value of num_rolls so that results_1 has the results of rolling a die ten times.

3.

Using the range() function, create a 12-sided die called die_12. Use similar logic as die_6.

4.

Simulate rolling die_12 ten times, and save the rolls as results_2. Use the np.random.choice() function to simulate the rolls, and be sure to print out your results!