Let X N(0, 9) have mean 0 and variance 9. Find the expected value of X2(X...

Question

Question

Let X N(0, 9) have mean 0 and variance 9. Find the expected value of X2(X +1).

Answer 1

Answer #1

X~normal distribution

E(X)=0 ,V(X)=9

$V(X)=E(X^2)-[E(X)]^2$

$9=E(X^2)-0$

$E( X 2) = 9$

$E(X^3)=0$

# for normal distribution

$mu_{2r+1}=0$

Where r=0,1,2......

$E[X^2(X+1)]=E[X^3+X^2]$

$=E[X^3]+E[X^2]$

=0+9

=9

Answer 2

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