Please Answer True and False only if you are confident and please provide reason
ID: 3358544 • Letter: P
Question
Please Answer True and False only if you are confident and please provide reasoning.
2 (15) Indicate whether the following are true or false (a) COV(X, Y) = COV(Y, X) for all random variables X and Y (b) If two random variables are jointly Gaussian, they must be marginally Gaussian. (c) If two random variables are marginally Gaussian, they may be jointly Gaussian. (d) The pdf of X+Y always equals the convolution of the pdfs of X and Y (e) If two random variables are independent, they must be uncorrelatedExplanation / Answer
(a) True. Because of symmetric propertiy
(b) True.It can be proved that if f(x,y) be joint pdf of Gaussian distribution, then the marginal pdfs fX(x) and fY(y) are also Gaussian.
(c) True. It can also be proved that if X and Y are two Gaussian variates, then their joint pdf f(x,y) is joint pdf of Gaussian.
(d) False.
(e) True. But the reverse is not true.