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1. If Y has a gamma distribution with shape a and rate its PDF is fy (y): ya-¹e-λya I(a) for y > 0. (a) Determine a formula for E{Y-k} which is valid for all (positive) integers k such that 0 2). (c) Use the CDF method to derive the PDF of X.

1. If Y has a gamma distribution with shape a and rate its PDF is fy (y): ya-¹e-λya I(a) for y > 0. (a) Determine a formula for E{Y-k} which is valid for all (positive) integers k such that 0 2). (c) Use the CDF method to derive the PDF of X.

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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1. If Y has a gamma distribution with shape a and rate its PDF is fy (y) = ya-¹e-ya r(a) for Y > 0. (a) Determine a formula for E{Y-k} which is valid for all (positive) integers k such that 0 <k <a. (b) The random variable X = Y-¹ is said to have an inverse Gamma distribution. Use the previous part to determine the mean and variance of X (for a > 2). (c) Use the CDF method to derive the PDF of X.
Transcribed Image Text:1. If Y has a gamma distribution with shape a and rate its PDF is fy (y) = ya-¹e-ya r(a) for Y > 0. (a) Determine a formula for E{Y-k} which is valid for all (positive) integers k such that 0 <k <a. (b) The random variable X = Y-¹ is said to have an inverse Gamma distribution. Use the previous part to determine the mean and variance of X (for a > 2). (c) Use the CDF method to derive the PDF of X.
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