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 T(k) ok to -1 ¹e-/, if x > 0, and otherwise, T(k)= 100 a x-le- - dr 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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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
I(K)0k
{
k-1-2/0
∞
if x > 0, and
otherwise,
T(k)=
x-le- dx
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 4(x) = 1 I(K)0k { k-1-2/0 ∞ if x > 0, and otherwise, T(k)= x-le- dx 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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