Question

Let X be a random variable with a finite mean μ and such that E[(X - μ)^2] is finite. Then the variance of X is defined to be E[(X - μ)^2], denoted as σ^2. Using this expected value expression: σ^2 = E[(X - μ)^2], show that the variance, σ^2 = E(X^2) - μ^2.

Name: let x be a random variable with finite mean mu and such that ex mu2 is finite then the variance of x is defined to be ex mu2 denoted as sigma2 using this expected value expression sigma2 ex 26678
Uploaded: 2022-05-16T15:07:09-08:00
Duration: 2 min 30 s
Channel: David Nguyen
Description: let x be a random variable with finite mean mu and such that ex mu2 is finite then the variance of x is defined to be ex mu2 denoted as sigma2 using this expected value expression sigma2 ex 26678

          Let X be a random variable with a finite mean μ and such that E[(X - μ)^2] is finite. Then the variance of X is defined to be E[(X - μ)^2], denoted as σ^2. Using this expected value expression: σ^2 = E[(X - μ)^2], show that the variance, σ^2 = E(X^2) - μ^2.

Added by James S.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert David Nguyen

05/16/2022

Step 1

This can be expanded to E[X^2 - 2Xμ + μ^2] by applying the formula (a - b)^2 = a^2 - 2ab + b^2. Show more…

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Let X be a random variable with a finite mean μ and such that E[(X - μ)^2] is finite. Then the variance of X is defined to be E[(X - μ)^2], denoted as σ^2. Using this expected value expression: σ^2 = E[(X - μ)^2], show that the variance, σ^2 = E(X^2) - μ^2.