Random variables - Exercise set 1

This exercise set contains some solved exercises on discrete random variables and probability mass functions. The theory needed to solve these exercises is introduced in the lecture entitled Random variables.

Exercise 1.1

Let be a discrete random variable. Let its support be:

Let its probability mass function be:

Calculate the following probability:

Solution

Exercise 1.2

Let be a discrete random variable. Let its support be the set of the first natural numbers:

Let its probability mass function be:

Compute the probability:

Solution

Exercise 1.3

Let be a discrete random variable. Let its support be:

Let its probability mass function be:where is the binomial coefficient.

Calculate the probability:

Solution