MATH 230 Final, Summer 2002

AMERICAN UNIVERSITY of BEIRUT MINLH/STAT 230. FINAL EXAM Time = 1 hour 30 minutes Aug 26, 2002 You are allowed to use a calcnlator and one formula sheet of discrete and coutinnous distributions! i. A bridge hand is defined as 13 cards selected at random without re- placement from a deck of 52 playing cards. (a) What is the probability of bemg dealt at random a bridge hand that does not contain a spade? (5 pts) (bj) What is the probability that a bridge hand contains exactly 5 hearts? (5 pts) fe) Find the probability that a bridge hand contains at most one ace. (9 pts) 2. Consider independent tosses of a fair coin. Find the probability that the fifth head is observed on the tenth toss. (5 pts) Find the moment generating friction, mean. aud variance if the pdf of Nin f(r) = U1 2)(2/3)" ifs = 1,2,3..... (10 prs) OT ECN*) = 28 for bh = 1,2.3..., find A(t). the moment generating funetion of Vo Cau vou determine the pdf of XN’ (10 pts) Find the point at which a chi-square with r degrees of freedom pdf obtains its manxiutun when ¢ > 2 (10 pts) Let VY have a uniform distribution U(-1.3). Find the pdf of ¥ = 47, (10 pts) © The pdf of Nis f(r) = wt ifO<ar <1. Ler} = -/n(r). Find the distribution of Yo ol0 pts}