Suppose E(X) = 5 and E[X(X – 1)] = 27.5, find \in (x^2 ) and the variance.

kuCAu

kuCAu

Answered question

2021-09-06

Suppose E(X)=5 and E[X(X1)]=27.5, find (x2) and the variance.

Answer & Explanation

averes8

averes8

Skilled2021-09-07Added 92 answers

We have the following properties: E(X+Y)=E(X)+E(Y)
V(X)=E(X2)[E(X)]2
So, if we have that E[X(X1)]=27.5, we can write them using the first property as: E(X(X1))=27.5
E(X2X)=27.5
E(X2)E(X)=27.5
Then, replacing E(X) by 5 and solving for E(X2) we get: E(X2)5=27.5
E(X2)=27.5+5
E(X2)=32.5
Finally, using the second property and replacing E(X) by 5 and E(X2)by32.5, we get that V(X) is equal to: V(X)=32.552
V(X)=32.525
V(X)=7.5
Finally answer: E(X2)=32.5
V(X)=7.5
E[X(X1)]=E(X2)E(X)
V(X)=E(X2)[E(X)]2

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