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Unformatted text preview: the probability that a. ( 10 pts ) Their sum is even b. ( 10 pts ) Their product is even. 3. ( 20 points ) X is a continuous random variable with cdf F X ( x ) = 1(1x ) 2 for 0 x 1, with F X ( x ) = 0 for x 0, and F X ( x ) = 1 for x 1. a. ( 10 pts ) Find the pdf of X . b. ( 10 pts ) Let Y = 2( X + 1) 2 . Find the cdf of Y . 4. ( 20 points ) A random integer N from 1 to 10 is chosen uniformly at random. a. ( 10 pts ) The random variable X denotes the number of distinct prime factors of N . (So if N = 8 = 2 3 , X = 1). Find the pmf of X . b. ( 10 pts ) Another random integer N from 1 to 10 is also chosen uniformly at random. Find the probability that N > 2 N . 5. ( 20 points ) Is it possible for two events A and B with P (A) , P (B) > 0 to be both mutually exclusive and independent. Why or why not? Scrap Page (please do not remove this page from the test packet)...
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This note was uploaded on 10/26/2010 for the course MATHCS Math 316 taught by Professor Dr.paulhorn during the Fall '10 term at Emory.
 Fall '10
 Dr.PaulHorn

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