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# Let X and Y be independent (strictly positive) gamma

ISBN: 9780131453401 223

## Solution for problem 9 Chapter 8.4

Fundamentals of Probability, with Stochastic Processes | 3rd Edition

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Fundamentals of Probability, with Stochastic Processes | 3rd Edition

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Problem 9

Let X and Y be independent (strictly positive) gamma random variables with parameters (r1, ) and (r2, ), respectively. Define U = X + Y and V = X/(X + Y ). (a) Find the joint probability density function of U and V . (b) Prove that U and V are independent. (c) Show that U is gamma and V is beta.

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Elementary Statistics Notes Amanda Selly 8/29/2016  Mean: average  To find the mean you add up all the values and then divide by the number of values you have o Population mean: µ= x1+x2+x3+…+xN/N µ= Σx/N o Sample mean: ~x= x1+x2+x3+…+xn/n µ= Σx/n Please note that sample mean is indicated by an x with a bar on...

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Let X and Y be independent (strictly positive) gamma

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