STAT 233 Exam 1, Fall 2003

-AMERICAN UNIVERSITY OF BE1RU.T STAT 233, Quiz I March 27, 2003 Time = 50 minutes You are allowed to use a calculator and one formula sheet.! O ~ e t the events Amd B have P(A) = 0.5 and P(A U B) = 0.7'. (a) Find P(B) if A and.B are independent. [5 pts] (b) Find P(B) if P(A[B) = 0.5. [5 pts] 2. Let the events A and B have P(AIB) = P(A*(B') = P(B*) = 0.95. Can you determine P(BIA)? [lo pts] . . @A fair rain is tossed four independent times Let X denote the number . of times a head is followed immediately by a tail. Find the probability density function, f(z), the cumulative distribution function,. F (z), md . the moment generating function, ilk (t). [ I 0 pts] single ,die is tossed;: then ic_ coins &e tossed, where k is t h e number ,. . . . . . .. J shown on the.die. What is the probability of getting exactly 2 heads? [ l o pts] . . : . . 5. Does there exists a. continuous random variable X with mean ,ux a i d standard deviation such that P(px - 2uly 5 X $ px t 2ox) = 0.6? Dr p*] www.amal-aub.org