Question

1. If the random variable Y has the Gamma distribution with a scale parameter $eta$, which is the parameter of interest, and a known shape parameter $alpha$, then its probability density function is $qquad f(y; eta) = frac{eta^{alpha}}{Gamma(alpha)} y^{alpha - 1} e^{-eta y}$, for $y > 0$ Show that this distribution belongs to the exponential family. Find E(Y) and var(Y).

          1. If the random variable Y has the Gamma distribution with a scale parameter $eta$,
which is the parameter of interest, and a known shape parameter $alpha$, then its
probability density function is
$qquad f(y; eta) = frac{eta^{alpha}}{Gamma(alpha)} y^{alpha - 1} e^{-eta y}$, for $y > 0$
Show that this distribution belongs to the exponential family. Find E(Y) and
var(Y).

$1. If the random variable Y has the Gamma distribution with a scale parameter eta, which is the parameter of interest, and a known shape parameter alpha, then its probability density function is qquad f(y; eta) = fraceta^alphaGamma(alpha) y^alpha - 1 e^-eta y, for y > 0 Show that this distribution belongs to the exponential family. Find E(Y) and var(Y).$

Added by Steven W.

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