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
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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
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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