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3. If X ~ Nga ?2), what is the median of X? Justify your answer (this does not have to be a proof). 4. If Y ~ Gamma(?, ?) , show that (a) E(Y)-??. (b) E(Y2)-?2(z + 1)a (c) V(Y)-??2

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Answer #1

Note: The gamma function satisfies many useful relationships, in particular,

\Gamma{(\alpha+1)} = \alpha \Gamma{(\alpha)}, \, \, \, \, \, \, \, \,\, \alpha > 0

\Gamma{(\alpha+2)} = (\alpha+1)\alpha \Gamma{(\alpha)}, \, \, \, \, \, \, \, \,\, \alpha > 0

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