Thread: a question abt covariance

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

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 be the pdf of Z.

Then because is an odd function.