Z~N(0,1), Let X1=Z, X2=Z^2, find cov(X1,X2). Cov(X1,X2)= E(X1*X2)-E(X1)E(X2)= E(Z^3)-E(Z)E(Z^2)= E(Z^3) bcoz E(Z)=0, does it mean E(Z^n)=0 ??? anyone can explain ?? thanx
Last edited by solskjaer; Nov 22nd 2008 at 05:31 PM.
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Originally Posted by solskjaer Z~N(0,1), Let X1=Z, X2=Z^2, find cov(X1,X2). Cov(X1,X2)= E(X1*X2)-E(X1)E(X2)= E(Z^3)-E(Z)E(Z^2)= E(Z^3) bcoz E(Z)=0, does it mean E(Z^n)=0 ??? anyone can explain ?? thanx Let $\displaystyle f(z)$ be the pdf of Z. Then $\displaystyle E(Z^{2n+1}) = \lim_{a \rightarrow + \infty} \int_{-a}^{a} z^{2n+1} f(z) \, dz = 0$ because $\displaystyle z^{2n+1} f(z)$ is an odd function.
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