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Chapter 4: Q.4.8 (page 170)

Let Xbe a random variable having expected value 渭and variance 蟽2. Find the expected value and variance ofY=X-渭蟽.

Short Answer

Expert verified

Mean is 0, and variance is 1.

Step by step solution

01

Given information

Let X be a random variable having expected value 渭 and variance 蟽2.

02

Calculation

Utilizing the linearity of expectation, we have that

EY-渭蟽=1蟽(E(Y)-E(渭))=1蟽(渭-渭)=0

And using the effects of the Variance (adding a constant accomplishes not change the variance and multiplying by a constant increase the variance by the square) we have that

VarY-渭蟽=1蟽2Var(Y)=1蟽2脳蟽2=1

03

Final answer

The expected value and variance are0,1.

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