Show that any polynomial expression in X 1 ,,X p , say can be expressed as a homogeneous polynomial in X 0 ,X 1 ,,X p Q4 p ijkl 0 bijklX iX jX kX l 4 , where X 0 1 Give expressions for the coefficients b in terms of the as Find E(Q4) and var(Q4) and express the results in terms of the as

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Question: Show that any polynomial expression in X 1 ,,X p , say can be expressed as a homogeneous polynomial in X 0 ,X 1 ,,X

Show that any polynomial expression in X 1

,…,X p

, say can be expressed as a homogeneous polynomial in X 0

,X 1

,…,X p

Q4 =

∑

ijkl=0 bijklX iX jX kX l/4!, where X 0 = 1. Give expressions for the coefficients b in terms of the as. Find E(Q4) and var(Q4) and express the results in terms of the as.

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