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m218_f09_mt1_practice3

m218_f09_mt1_practice3 - it will consist of 2 women and 1...

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Midterm 1, Practice problems, Part 3 #1 The joint distribution of random variables X and Y is given below X Y 0 1 -1 0.12 0.08 0.2 0 0.06 0.04 0.1 1 0.42 0.28 0.7 0.6 0.4 a) Write down the distribution of X alone. b) Write down the distribution of Y alone. c) Are the events {X=-1} and {Y=1} independent? d) Are X and Y independent? e) Find Cov(X,Y). #2
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#4 #5 A bag of marbles contains 6 red marbles and 2 black marbles. a) How many samples of size 4 are there? b) How many samples of size 4 are there that consist of 3 red marbles and 1 black marble? c) If a simple random sample of size 4 is selected from the bag, what is the probability that it will consist of 3 red marbles and 1 black marble? #6 Consider a population consisting of 20 women and 10 men. a) How many samples of size 3 are there? b) How many samples of size 3 are there that consist of 2 women and 1 man? c) If a simple random sample of size 3 is selected from this population, what is the probability that
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Unformatted text preview: it will consist of 2 women and 1 man? #7 A committee consisting of 5 people is to be chosen from a group of 20 people. a) How many different committees are possible? b) How many committees are there that include both Aaron and Bernadette? #8 100 people participate in a raffle that will have 3 winners. How many different combinations of 3 winners are possible? #9 A woman is attacked by two assailants. A day later the police show her a line-up of 7 suspects. The line-up includes the 2 guilty people. a) How many ways can the woman choose 2 people out of the line-up? b) How many ways can the woman choose 2 people out of the line-up exactly one of whom is guilty? #10 The qualified applicant pool for 6 management trainee positions consists of 7 women and 5 men. a) How many different groups of applicants can be selected for the positions? b) How many of those groups consist entirely of women?...
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