Probability Distributions

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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.

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():

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

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

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

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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.