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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 1 y(x) = (k)0k -¹e-2/0, if z>0, and otherwise, T(k) = ² a is the gamma function. For every k ≥ 1,0 > 0, find the point at which p(x) has its maximum. Hints: The algebra can be simplified by appropriate use of logarithms. 2k-¹e-zdr

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 1 y(x) = (k)0k -¹e-2/0, if z>0, and otherwise, T(k) = ² a is the gamma function. For every k ≥ 1,0 > 0, find the point at which p(x) has its maximum. Hints: The algebra can be simplified by appropriate use of logarithms. 2k-¹e-zdr

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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 y(x) = 1 T(k) ok --¹e-/, if x > 0, and otherwise, T(k) = √√ pk-le-d is the gamma function. For every k ≥ 1, 0 > 0, find the point at which p(x) has its maximum. Hints: The algebra can be simplified by appropriate use of logarithms.
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 y(x) = 1 T(k) ok --¹e-/, if x > 0, and otherwise, T(k) = √√ pk-le-d is the gamma function. For every k ≥ 1, 0 > 0, find the point at which p(x) has its maximum. Hints: The algebra can be simplified by appropriate use of logarithms.
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