MAT521-2007Fallb - 5 J.1- I NAME: FINAL MATS21 FALL 2007 1....

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5J.1- I NAME: FINAL MATS21 FALL 2007 1. A class consists of 15 girls and 20 boys. (a) In how many different ways can a class president, vice-president, treasurer, and secretary of defense be randomly selected? (b) Suppose instead that a committee of 4 is to be randomly selected from the class. How many different committees can be formed? (c) What is the probability that exactly 2 boys and 2 girls are selected for the committee? Date: December 6, 2007.
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2 VERCHOTA 2. Let X and Y be random variables with joint p.d.f. f(x )={ 6xy2, O<x~l,O<y<l , y 0, otherwIse (a)Find the marginalp.d.J. ofX. b(x) = (b) Compute the conditional p.d.J. ofY given that X=x, g2(ylx) (c) Compute Pr( Y < ~ I X = .13) = (d) Are X and Y independent? Inclnde a description of the domain for any formulas in your answers.
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3 FINAL MAT52! FALL 2007 3. Let X and Y be independent random variables with E(X) = I, E(Y) = 1 and E(X 2 ) = 2, ECy2) = 3. (a) Compute E(X _ y)2) = (b) Compute Var(X - Y)= 4. (a) A fair coin (probability of obtaining a Head is 112) is tossed 40 times. What is the expected number of Heads obtained? What is the variance of the number of Heads? (b) A biased coin with probability of obtaining a Head equal to 115 is tossed 50 times. What is the expected number of Heads obtained? What is the variance of the number of Heads? (c) Suppose the two coins are tossed independently of one another.
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MAT521-2007Fallb - 5 J.1- I NAME: FINAL MATS21 FALL 2007 1....

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