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Chapter 7: Q.7.3 (page 354)

If Xand Y are independent and identically distributed with mean 渭and variance 蟽2, find

E(X鈭�Y)2

Short Answer

Expert verified

The value of E(X鈭�Y)2is

E(X鈭�Y)2=2蟽2

Step by step solution

01

Step 1:Given Information

XandYare autonomous and identically allocated with mean渭and variance 蟽2.

02

Step 2:Explanation

E[X]=E[Y]=渭

Var(X)=Var(Y)=蟽2

Var(X)=EX2鈭�(E[X])2

EX2=Var(X)+(E[X])2

=蟽2+渭2

X and Y are independent,

E(X鈭�Y)2=EX2鈭�2XY+Y2

=EX2鈭�2E[X]E[Y]+EY2

=蟽2+渭2鈭�2渭渭+蟽2+渭2

=2蟽2+2渭2鈭�2渭2

=2蟽2

03

Step 3:Final Answer

E(X鈭�Y)2=2蟽2

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