Answered: 1. If Y has a gamma distribution with… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section: Chapter Questions

Problem 9T

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Question

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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