An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" () which we write hth, ttt, etc. For each outcome, let N be the random variable counting the number of tails in each outcome. For example, if the outcome is htt, then N (htt) = 2. Suppose that the random variable X is defined in terms of N as follows: X=2N²-4N-4. The values of X are given in the table below. Outcome Value of X Value X of X P(X=x) ttt hht hth tth tht 6-6 -4 -4 htt thh hhh -4 2 Calculate the probabilities P(X=x) of the probability distribution of X. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row. 0 -4-6 X S

q13- X and Y are two independent random variables. We know V(X) = 26.43 and V(Y) = 23.67, then V(8X + 5Y) is: a. 862.68 b. 2283.27 c. 329.79 d. 16490.91

Suppose that X is a N(3,4) random variable and suppose that Y=5X+2. Determine P(Y>18.5).