Exercise 7.(a) Suppose a fair coin is flipped n times. Each coin toss costs d dollars and the reward inobtaining X heads is aX2 + bX. Find the expected value of the net reward.(b) Suppose that the reward in obtaining X heads is instead aX for a > 0. Find the expectedvalue of the reward.

Exercise 6.Two dice are tossed and we let X be the difference in the number of dots facing up.(a) Find and sketch the pmf of X.(b) Find the probability that |X| k for all k.

Exercise 3:A binary communication channel has a probability of bit error of 10^-6. Suppose that transmission occur in blocks of 10,000 bits. Let N be the number of errors introduced by the channel in a transmission block.

a) Find P[N = 0],

b) Find P[N <=3].

c) For what value of p will the probability of 1 or more errors in a block be 99%

Exercise 5;Let Y = |X| be the output of a full-wave rectifier with input voltage X.

(a) Find FY (y) by finding equivalent event of {Y y}. Find fY (y) by differentiating

FY (y).

(b) Find fY (Y ) directly and compare with your answer to part (a).

(c) Give a simplified expression for fY (y) if fX(x) is an even function of x