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()`

:

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 code as-is 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!