Question Video: Variance of a Discrete Random Variable | Nagwa Question Video: Variance of a Discrete Random Variable | Nagwa

# Question Video: Variance of a Discrete Random Variable Mathematics • Third Year of Secondary School

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Let π denote a discrete random variable. Given that πΈ(π) = 15 and Var(π) = 26, find πΈ(πΒ²).

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### Video Transcript

Let π denote a discrete random variable. Given that πΈ of π equals 15 and Var of π equals 26, find πΈ of π squared.

Letβs begin by recalling what each of these pieces of notation mean. πΈ 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. πΈ 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 itβs 15 β and the variance of π β itβs 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 πΈ of π squared by adding 225 to each side. That gives 251 is equal to πΈ 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 πΈ of π squared is 251.

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