MATH3334 Exam 2

MATH3334 Exam 2 - 3. The monthly worldwide average number...

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Name:______________________ Practice Exam 2 Math 3334 Fall, 2007 1. Suppose a pair of dice is rolled. Let X denote the sum of the numbers on the upturned faces of the dice. (a) Exhibit the probability mass function of X as a table of values. (b) Find the value of E(X). (c) Find the value of Var(X). 2. Suppose an urn contains 1 white and 2 black balls. Balls are randomly selected, one at a time, until a black one is obtained. We assume that each selected ball is replaced before the next one is drawn. Let X be the number of draws needed to obtain a black ball. (a) What is the value of P(X=3)? (b) Find the value of E(X). (c) Find the value of Var(X).
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Unformatted text preview: 3. The monthly worldwide average number of airplane crashes of commercial airlines is 3.5. Assume that the number of such crashes is a Poisson random variable. What is the probability that there will be (a) at least 2 such accidents in the next month? (b) at most 1 accident in the next month? 4. The distribution function of a random variable X is given by: 3 if , 1 3 2 if 1/2, 2 1 if , 3 / 1 1 if , ) ( < < < = x x x x x F Find: (a) P(X=1) (b) P(X=3/2) (c) P(X=2) (d) E(X) 5. A graduate class consists of six students. What is the probability that exactly three of them were born either in April or in October?...
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