Unformatted text preview: 3. Suppose X 1 , . . . , X 12 are i.i.d. uniform(5 , 19), and let ¯ X = 121 ∑ 12 i =1 X i . Use the central limit theorem to approximate the probability Pr( ¯ X ≤ 13). 4. Suppose X ∼ Poisson(2) and Y ∼ Poisson(1) are independent. ±ind Pr( X + Y ≤ 3). 5. At a nuclear plant, (minor) accidents occur to a Poisson process with a rate of one every two years. (a) What is the probability that the time between successive accidents is greater than two years? (b) What is the probability that 4 or more accidents will occur in a twoyear interval? (c) What is the mean number of accidents in ten years? (d) Suppose that a year has passed since the last accident. What is the probability that the next accident will occur at least three years from now? 6. [Will not be graded] Exercises 1, 2, 6, 7, 14, 19, 21, 30, 38, 39, 40, and 52 from Chapter 5 of BCN&N....
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 Spring '08
 ALEXOPOULOS
 Poisson Distribution, Mean, resource cycle, accurate point estimators, initial waiting area

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