1) Suppose Y 1 , . . . , Y n is random sample from N(3, 2 ). Then, b 2 = Pn i=1(

Question

1) Suppose Y1, . . . , Yn is random sample from N(3, 2 ). Then, b 2 = Pn i=1(Yi3)2 /n is a sufficient and unbiased estimator of 2 . Yes / No.

2) Suppose Y1, . . . , Yn is a random sample from Poisson (). Then, both the sample mean, Y¯ , and the sample variance, S 2 = Pn i=1(YiY¯ ) 2 /n1 , are the MLEs of . Yes / No

3)The MLE of a parameter always exists. Yes / No

(h) Suppose Y1 Yn is random sample from N(3,02). Then, O is a sufficient and unbiased estimator of o2 Yes No. (i) Suppose Y1, n is a random sample from Poisson (0). Then, both the sample mean Y, and the sample variance s2- are the MLEs of 0. Yes No n-1 No Yes

Explanation / Answer

H] answer is true

Yes it is unbiased estimator of variance

I] yes s2 is unbiased estimator of possible parameter

J] mle of parameter doesn't exist always

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