15b_00f_qe

15b_00f_qe - 15B Weekly Quizzes Q1. A family has 4 girls...

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15B Weekly Quizzes Fall 2000 Q1. A family has 4 girls and 3 boys. (a) How many ways can they sit in a row? (b) How many ways can they sit in a row if boys and girls must alternate? Q2. How many ways can t teams each of size s be made from st people? The teams have no names or other distinguishing features. Three versions were given depending on student ID number: s =2 ,t =4; s =3 =3; s =4 . Q3. Let A , B and C B be sets. We make B A into a probability space by selecting functions from A to B uniformly at random. (a) What is the probability that a random f is an injection? (b) What is the probability that f ( A ) C for a random f ? Express answers in terms of a = | A | , b = | B | and c = | C | . Q4. A permutation is given in cycle form. Write it in two line form and find its tenth power. Three versions were given depending on ID number. (1 , 3 , 7)(2 , 9 , 4 , 8)(5 , 6) (1 , 2 , 5 , 4)(3 , 9)(6 , 8 , 7) (1 , 7)(2 , 4 , 9 , 6)(3 , 8 , 5) . Q5. Suppose X and Y are random variables with mean 0 and variance σ 2 . Suppose that Cov( X, Y )= c . Express the following in terms of σ and c .
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15b_00f_qe - 15B Weekly Quizzes Q1. A family has 4 girls...

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