P 11. a) X has continuous cumulative distribution function F(z). Calcu- late P(q1 4|Y > 2). d) If X ~ Poisson(2), calculate E[X?]. e) X1 ~ Bin(3,1/2) and X, ~ Bin(2,1/2) are independent. Deter- mine P(X, + X, = 2). f) What is the mean and variance of X 2V if X ~ N(1,4), ~ N(-2,1) are independent? g) What interval describes within three standard deviations from the mean for X ~ N(1,0.36)? h) Find (zp045) without a table. i) We flip a fair coin 10 times. Which is more likely? HHTHHTHHHT, TTTHHHHHHH or TTTTTTTHHH ? j) We flip a coin until a Head (H) turns up. While experimenting, we obtain the data 5, 7, 5, 5, 3, 6, 5, 6, 7, 4 equal to the number of coin flips needed to turn up the first H. Estimate the probability p of turning H for this coin