### Video Transcript

Let π denote a discrete random variable. Given that πΈ of π equals 15 and Var of π equals 26, find πΈ of π squared.

Letβs begin by recalling what each of these pieces of notation mean. πΈ of π, first of all, is the expectation or expected value of the discrete random variable π. It is its average value, and we often denote this using the Greek letter π. Var of π stands for the variance of π, which is a measure of spread of the probability distribution. We denote this using the Greek letter π squared or sometimes π sub π squared if there are multiple variables in the same problem. πΈ of π squared is the expected value of π squared. That is, we square the values of the discrete random variable and then find their expectation.

These three quantities are related by the following formula. The variance of π is equal to the expected value of π squared minus the expected value of π squared. As we know the expected value of π β itβs 15 β and the variance of π β itβs 26 β we can substitute these values into this formula to find the expectation of π squared. We have then 26 is equal to the expectation of π squared minus 15 squared. 15 squared is 225. And then, we can solve this equation for πΈ of π squared by adding 225 to each side. That gives 251 is equal to πΈ of π squared.

So, by recalling the definition of the variance of a discrete random variable and then forming and solving an equation, we found that πΈ of π squared is 251.