Please see the problem in the attachment.

1. State TRUE or FALSE by giving reasons [5 points each] You must state a correct reason to get credit. No partial credit. (a) Let Y1, Y2 and Y3 be three continuous random variables with the following joint PDF: fy1, Y2, Y's ( y1, y2, y3) if y3 > y2 > y1 2 0 0 otherwise The MMSE estimate of Y1 from Y2 and Y is given by Y2/2. (b) Consider a sequence of independent and identically distributed random variables X1, X2, X3, . .., Xn, . ... . The PMF of Xi is given by P(Xi = 1) = P(Xi = -1) = 4, and P(Xi = 0) = 5. Let Zn = Et Xi. The CDF of Zn converges to that of Gaussian with zero mean and unit variance