Question

Consider the random variables X, Y and Z, which are given to be pairwise uncorrelated (i.e., X and Y are uncorrelated, X and Z are uncorrelated, and Y and Z are uncorrelated). Suppose that

E[X]=E[Y]=E[Z]=0,

E[X2]=E[Y2]=E[Z2]=1,

E[X3]=E[Y3]=E[Z3]=0,

E[X4]=E[Y4]=E[Z4]=3.

Let W=a+bX+cX2 and V=dX, where a,b,c, and d are constants, all greater than 0.

Find the correlation coefficients ρ(X−Y,X+Y), ρ(X+Y,Y+Z), ρ(X,Y+Z) and ρ(W,V).

ρ(X−Y,X+Y)=- unanswered
ρ(X+Y,Y+Z)=- unanswered
ρ(X,Y+Z)=- unanswered

Answer 1

ρ(X−Y,X+Y)= 0

ρ(X+Y,Y+Z)= 0.5

ρ(X,Y+Z)= 0

ρ(W,V)= (b)/((b^2+2c^2)^0.5)

hope it helps! I am needing the other answers to the whole problem set