STAT 233 Final, Spring 2004

bo wo 4. en OF VEFROT AMERICAN UNIVERSITY of BEIRUT STAT 233, Final Exam A; be indepencens events with probabilizies 1/3, 1/4 Compute P(.4; U 42 U As). ‘exercise number 1.120) on A tosses a coin and person B rolls a lie tependenily until one head or one of tne numbers i, 2, 3, 4 appears, ac waich time the game is stopped. Person A wins with che hea B wins witn one of the numbers 1. 2, 3, 4. Compute the or that A wins the game. :exercise number 1.123] O° ion & om — = oq <a The probabilities that the independence events A, B, and C will occur are 3/4, 1/2, and i/4. What is the probability that at least one will occur. exercise number 1.133) Let X and Y be two independent dinomial random variables with pa- rameters n and p= 1/2. show that (In! . . (2n}! ” [exercise number 3.32] yo eV 6 Me you may Ue the Lokd, 2. ( x Yaerie ~ ( ~ ° Let the random variables XY, and Xj be a random sampie of : the p.df, f(z} =1if0 <2 < 1, zero elsewhere. Find the distribution of the random variable Y, = X,+X. and the distribution of the random variable ¥; = X, — Xy. [example 4 of chapter 4) + = 2 from Let X; and X) be a random sample of size 2 from a distribution wh nas the.p.d.i f(r) =1ifO <x <1, O elsewhere. Find the 5. the random variable Y = (> fexercise 4.14: Hint: Consider two cases when 0 < y <land whenl<y<cxo