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Unformatted text preview: Y where P ( Y = θ ) = 1. Question 5: (5 marks). In a grocery store checkout line, it has been found that the average time to process a customer is a r.v. X with a mean of 5 minutes and a standard deviation of 2 minutes. Use the CLT to approximate 1 the probability that 50 customers can go through the checkout line in less than 4 hours. Question 6: (8 marks). Let Y ∼ Uniform[0 , 1], and let X n = Y n . Show that { X n } converges with probability 1 to the degenerate r.v. X where P ( X = 0) = 1. Question 7: (5 marks). Let X 1 ,X 2 ,... be an inﬁnite sequence of continuous r.v.’s such that f X n ( x ) = ( ( n + 1) x n , < x < 1 , , otherwise. Show that { X n } converges in distribution to the degenerate r.v. X where P ( X = 1) = 1. 2...
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 Spring '11
 peskun
 Math, Standard Deviation, Probability theory, 2 minutes, 4 hours

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