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15b_01f_me

15b_01f_me - h X,Y for two random variables X and Y(a Find...

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Math 15B Midterm Exam 26 October 2001 Please put your name and ID number on your blue book. The exam is CLOSED BOOK, but a PAGE OF NOTES IS ALLOWED. Calculators are NOT ALLOWED. You need not evaluate binomial coeﬃcients. You must show your work to receive credit. 1. Give an example of each of the following or explain why it cannot be done. (a) A bijection from { 1 , 2 , 3 , 4 } to { a, b, c } . (b) A permutation of { 1 , 2 , 3 , 4 , 5 , 6 , 7 } that has a cycle of length 4 and also has a cycle of length 5. 2. A committee contains 7 women and 6 men. We want to form a subcommittee with 5 of these people. (a) How many ways can this be done? (b) How many ways can this be done if the subcommittee must contain at least 2 women and at least 2 men? 3. The table below gives the joint distribution function,
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Unformatted text preview: h X,Y , for two random variables X and Y . (a) Find the distribution functions f X for X and f Y for Y . (b) Are X and Y independent? (You must give a correct reason for your answer.) h X,Y Y=-1 Y=0 Y=+1 X=-1 1/6 1/6 X=0 1/3 X=+1 1/6 1/6 4. A deck of cards has 52 cards and 13 of these cards are spades. (a) I take seven cards at random from the deck. What is the probability that I get exactly three spades? (b) I take a card at random from the deck, note whether it is a spade, and put it back. If I do this seven times, what is the probability that I get a spade exactly three times? Suggestion : Think of spade and non-spade like bad and good. END OF EXAM...
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