Let X be a random variable and a real number. Show thatE(X - a)² = varX + (µ − a)²Hereμ = EX is the expected value of the random variable X and varX = E(X - μ)^2 is thevariance of the random variable X. Guidance: start from the representation-(X-a)^2 = (X µ + μ- a)^2 and group the right side of the representation appropriatelyinto the form (Z + b)^2, where Z is some random variable and b is a real number andopen the square. The task should be solved with the help of the expected value calculationrules.

E(X−a)2=E(X−μ+μ−a)2=E((X−μ)+(μ−a))2=E((X−μ)2+2(X−μ)(μ−a)+(μ−a)2)=E(X−μ)2+E(2(X−μ)(μ−a))+E(μ−a)2=E(X−…

Answered: Let X be a random variable and a real…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 93E

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