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Spring 2011 Homework 5 - Probability and Statistics for...

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Probability and Statistics for Engineering Homework 5 Spring 2011 (due Tuesday, March 1) (1) Completely simplify the value . (Keep it exact rather than getting a decimal / # $ ln approximation for it.) This should prove to be useful below. (2) Consider the following function , which is a density function for a continuous random 0 variable . \ 0ÐBÑ œ / ! Ÿ B Ÿ $ * % #B ln (a) Find the mean of directly (via integration, using the definition of the mean). Show \ all your work, including the details of the integration. Give your answer in exact both form (in terms of logarithms and/or exponentials, completely simplified) as a and decimal, rounded to four decimal places. (b) Find the moment generating function for . Show your work. There won't be much \ simplifying you can do at the end, and that's OK. (c) Find the mean of using the moment generating function. Show your work. \ Hint 1 . Of course, your answers for (a) and (c) should match. If they are not the same, don't change something randomly to force them to match.
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