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Let Y_1~Gamma(α=3,β=3), Y_2~Gamma(α=5,β=1), and W=2Y_1+6Y_2.

a) (9 pts) Find the moment generating function ofW Justify all steps b) (3 pts) Based on your result in part (a), what is the distribution of W(name and parameters)?

n 2N(O, I) 2. IfZ NO, 1), then Ux(1) 3. ItY Gmmaa,B) and W then Wx(n) - s, and i-1 7. ys~ Poisson(W (i-l, ,Rind) and U-ŽYi, then U-Poisson(XA) 8 If%-Gamma(a, β) (i-I, ,Rind) and U-ΣΥί , then U~Gamma( ,4 β).(Note: all same β) 9 If%-Exponential(8) (-1, ,n m) and U-Σ Yi , then U ~ Gamma( α , β).(Note : all same β) 10. yvi. Binomal(Bap) (i-1, m.ind) and U- ,Ý, , then U~ Binomial Дур) (Note: all same p ) 1 1. yvi and Y2 are independent rv s with mgi s mwt) andm½(t), then i-1 i-1 U+ Y has mgfmu(t)-my,(t)my(t), and

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Answer #1

Solution *a 1 Gt A. Hence mgf of MuteCompao.ng ngf of เง ม่¡th -thal of gomma distoibution of mit) - 1 เงิ follows gamma distitation with ROamah

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Let Y_1~Gamma(α=3,β=3), Y_2~Gamma(α=5,β=1), and W=2Y_1+6Y_2. a) (9 pts) Find the moment generating function ofW Justify all...
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