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Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
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In a medical experiment, a rat has been exposed to some radiation. The experimenters

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In a medical experiment, a rat has been exposed to some radiation. The experimenters believe that the rats survival time X (in weeks) has the pdf f(x) = 3x2 1203 e(x/120)3 , 0 < x < . (a) What is the probability that the rat survives at least 100 weeks? (b) Find the expected value of the survival time. Hint: In the integral representing E(X), let y = (x/120)3 and get the answer in terms of a gamma function.

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QUESTION:

In a medical experiment, a rat has been exposed to some radiation. The experimenters believe that the rats survival time X (in weeks) has the pdf f(x) = 3x2 1203 e(x/120)3 , 0 < x < . (a) What is the probability that the rat survives at least 100 weeks? (b) Find the expected value of the survival time. Hint: In the integral representing E(X), let y = (x/120)3 and get the answer in terms of a gamma function.

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