ALSON
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ALSON asked in 科學數學 · 1 decade ago

數學│機率論問題│請幫幫忙│20點│感恩感謝

Q:A random sample X1,X2,.....Xn of size n is taken from a Poisson distribution with a mean of λ,0<λ<∞.

(a) Show that the maximum likelihood estimator for λ is X^.

(b) Let X equal the number of flaws per 100 feet of a used computer tape.Assume that X has a Poisson distribution with a mean of λ.If 40 observations of X yielded 5 zeros ,7 ones,9 threes,5 fours,1 five,and 1 six,find the maximum likelihood estimate ofλ.

P.S:x^= ∧

X

Ans:(b)mean=89/40=2.225

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