2.(a)Let()w(o.()).Compute E[XY]without using Cov(X,Y)=o or corr(X,Y)=2.Hint:Rely on what you know about the conditionaldistribution of Y given X.[3](b)Now let()R~((R))where R takes values -1/2 and 1/2each with probability 1/2.i Computeμx=E[X]and uy=E[Y].[2]ii.Compute EXY and hence obtain Cov(X,Y).Hence compute the covari-ance matrix=Var(X)Cov(X,Y)Cov(X,Y)Var(Y)[3]iii.Compute Var(YX).Start with Var(YX)=Var(YX,R=1/2)P(R=1/2)+Var(YX,R=-1/2)P(R=-1/2).[3]iv.[TYPE:Decide whether the joint distribution of (X,Y)(which is not con-ditional on R)is Gaussian.Justify your decision carefully.[4]
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