## Question

###### Problem 2. (10 points) Consider Yi .....Y a random sample of observations from a poisson distribution...

Problem 2. (10 points) Consider Yi .....Y a random sample of observations from a poisson distribution with un- known parameter . Find the MLE for ..

## Answers

buku Ans Probability mass function of poisson dist? is Px (1j) = f exp if yj e Rx if yg & Rx The likelihood hinction is giren by ald, 41 42 .. Yn) = tf(yj, t) a it exp(-d) I dyj ja! 91! The log - likelihood function is giren by eld, 91 92 9n) = ln I exp(-d) L dyj JEA il Jo il = 2 in (exptd) I di [inf exp{-d)) – 101 914) +80 (09)] 2 [-d-en(43!) + 1; en C4)7 -nd- & in (y;!) ten (d) & ; The me is the solution of the follo maximization Problem d ong max 1(d, Boy, Y2::yn) The St order condition for a maximum is deld, g, Y... 4) = 0buku FACHA UKOCE 40,9,7...40) - d (and- 1014;!) Hola) e Yj val derivative be equal to zerro so we First get Answer: proximum likelihood estimator of dis

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