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Suppose that random variable X has a gamma(a, 1) distribution, for parameter a > 0. Let Y = 1/X. (a) Note that the PDF of gamma(a, B) is f(r; a, B) = gerora-le-=/B for r >0 and is 0 otherwise (a > 0,B > 0). Find the probability density function (PDF) ofY. Also find the expectation of Y. %3D

Suppose that random variable X has a gamma(a, 1) distribution, for parameter a > 0. Let Y = 1/X. (a) Note that the PDF of gamma(a, B) is f(r; a, B) = gerora-le-=/B for r >0 and is 0 otherwise (a > 0,B > 0). Find the probability density function (PDF) ofY. Also find the expectation of Y. %3D

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Functions of random variables. (a) Note that the PDF of gamma(a, B) is f(x; a, B) = gee -le-/P for x > 0 and is 0 otherwise (a > 0,B > 0). Find the probability density function (PDF) of Y. Also find the expectation of Y. Suppose that random variable X has a gamma(a, 1) distribution, for parameter a > 0. Let Y = 1/X. (Ъ) given by Suppose that a continuous random variable U has a cumulative distribution function (CDF), Fu, Fu (u) = exp{- exp{-u}} for – < u < 0. %3D Find the PDF of the random variable V defined as V = U?.
Transcribed Image Text:Functions of random variables. (a) Note that the PDF of gamma(a, B) is f(x; a, B) = gee -le-/P for x > 0 and is 0 otherwise (a > 0,B > 0). Find the probability density function (PDF) of Y. Also find the expectation of Y. Suppose that random variable X has a gamma(a, 1) distribution, for parameter a > 0. Let Y = 1/X. (Ъ) given by Suppose that a continuous random variable U has a cumulative distribution function (CDF), Fu, Fu (u) = exp{- exp{-u}} for – < u < 0. %3D Find the PDF of the random variable V defined as V = U?.
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