# Probability, S2, Var(X(8-X)) ?Watch

#1
X~U(3,7)

Y=X(8-X)

Finding E(Y) is ok and comes to 41/3.

How would you find Var(Y) ?

i tried E(Y²)=E([8X-X]²) and then using Var(Y)=E(X²)-E(X)² but that came out wrong.

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13 years ago
#2
(Original post by Infinity_Kev)

i tried E(Y²)=E([8X-X]²) and then using Var(Y)=E(X²)-E(X)² but that came out wrong.
should E(Y²)=E([8X-X²]²)? so you've just missed a square on the second X
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#3
Yeah i did that acctually and got

E(Y²)=64X²-16X³+X^4

I might have made a mistake somewhere i think il go through it again.
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#4
E(Y)=8*5 - comes to

now E(Y²) = E([8X-X²]²) = 64E(X²) - 16E(X³) + X^4

=

which comes to

so Var(Y)=

the book says answer is can anyone spot a mistake?????
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