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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.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.1: Solutions Of Elementary And Separable Differential Equations
Problem 54E: Plant Growth Researchers have found that the probability P that a plant will grow to radius R can be...
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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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