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.
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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![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1652026a-6ba6-42d7-9e35-ad3e7516e1ec%2F9608d377-f28c-4717-8260-bc0da00b26ae%2Fl9epbhf_processed.jpeg&w=3840&q=75)
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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