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hw4ma540

# hw4ma540 - Homework 4 1 Problem 1 Page 258 Let X be a...

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MA540 Page | 1 Homework 4 1) Problem 1 Page 258 Let X be a random number from . Find the probability density function of . Solution: Let F be the distribution function of Y . Clearly, . For , So 2) Problem 3 Page 258 Let X be a continuous random variable with density function What is the probability that X is within two standard deviations of the mean? Solution: Therefore,

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MA540 Page | 2 3) Problem 5 Page 259 Does there exist a constant for which the following is a density function? Solution: Fo r a ll , So, for no value of c , is a probability density function. 4) Problem 11 Page 259 The lifetime (in hours) of a light bulb manufactured by a certain company is a random variable with probability density function Suppose that, for all nonnegative real numbers a and b , the event that any light bulb lasts at least a hours is independent of the event that any other light bulb lasts at least b hours. Find the probability that, of six such light bulbs selected at random, exactly two last over 1000 hours. Solution:
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hw4ma540 - Homework 4 1 Problem 1 Page 258 Let X be a...

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