Exercise 16. The x²(v) distribution is a special case of Gamma distribution (not to be con- fused with gamma function; see below). The density function of the Gamma distribution with parameters and k is given by where 4(x) = { 0 1 r(k) ok T(k): xk-le-x/0 е = 2 ∞ • 10 201² is the gamma function. For every k ≥ 1, 0 > 0, find the point at which p(x) has its maximum. if x > 0, and otherwise, -x dx
Exercise 16. The x²(v) distribution is a special case of Gamma distribution (not to be con- fused with gamma function; see below). The density function of the Gamma distribution with parameters and k is given by where 4(x) = { 0 1 r(k) ok T(k): xk-le-x/0 е = 2 ∞ • 10 201² is the gamma function. For every k ≥ 1, 0 > 0, find the point at which p(x) has its maximum. if x > 0, and otherwise, -x dx
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Transcribed Image Text:Exercise 16. The x²(v) distribution is a special case of Gamma distribution (not to be con-
fused with gamma function; see below). The density function of the Gamma distribution with
parameters and k is given by
where
4(x) =
=
1
r(k) ok
pk-1
e
2
if x > 0, and
otherwise,
1.-x
a*-¹e-² dx
r(k) =
is the gamma function. For every k ≥ 1, 0 > 0, find the point at which y(x) has its maximum.
Hints: The algebra can be simplified by appropriate use of logarithms.
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