Lesson 17: Distributions of Two Discrete Random Variables

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Introduction

As the title of the lesson suggests, in this lesson, we'll learn how to extend the concept of a probability distribution of one random variable X to a joint probability distribution of two random variables X and Y. In some cases, X and Y may both be discrete random variables. For example, suppose X denotes the number of significant others a randomly selected person has, and Y denotes the number of arguments the person has each week. We might want to know if there is a relationship between and Y. Or, we might want to know the probability that X takes on a particular value x and Y takes on a particular value y. That is, we might want to know P(y).

Objectives

• To learn the formal definition of a joint probability mass function of two discrete random variables.
• To learn how to use a joint probability mass function to find the probability of a specific event.
• To learn how to find a marginal probability mass function of a discrete random variable X from the joint probability mass function of X and Y.
• To learn a formal definition of the independence of two random variables X and Y.
• To learn how to find the expectation of a function of the discrete random variables X and Y using their joint probability mass function.
• To learn how to find the means and variances of the discrete random variables X and Y using their joint probability mass function.
• To learn what it means that X and Y have a joint triangular support.
• To learn that, in general, any two random variables and Y having a joint triangular support must be dependent.
• To learn what it means that X and Y have a joint rectangular support.
• To learn that, in general, any two random variables and Y having a joint rectangular support may or may not be independent.
• To learn about the trinomial distribution.
• To be able to apply the methods learned in the lesson to new problems.