062/21

22.

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26.

160, ‏ملا . - . روكلا‎ be a random sample taken from a Poisson distribution with parameter A. Define

2
0) = 8 3 . Then the variance of an unbiased estimator of I(A) is larger than
2
5

1

ಬ ೫ ae

1
0) ಣಾ 0) na
Suppose ‏بولا‎ Xp, . . . X, are ೧ observations drawn randomly from the population having the 0.6.1.
1: 2 0 ly

2 =
£(x,0) = ae exp = ; 0 ‏م‎ where 6 > 0, then an approximate (1 - 0) level confidence interval
for 9 based on the maximum likelihood estimator of 9 namely 6-2 is

ட்‌. ட்‌ ட்‌. 3

A 6 A 6 A 6 A 8

^) 0 - 2/2 ‏جا دہج‎ B) ۱٥-2 ‏ا‎ 9+ 2५/२॥
6 2 4 a a ۳ a ம்‌

©) (98-2௨ ರ್ಯಾ, 0+ 22 [2 0) 8 - 2/2 ‏و2 + 8, جا‎ ರ್ಯ
A 5 5 5

0 0 0 0

Let ‏ہل‎ Xp, . . . , X, be independent random variables with X; following (ய ०2) distribution, i = 1, 2,...n.
Then the maximum likelihood estimator of ‏ىر‎ 15

24

27 dix,

n+1

A)

=
Let × Xp, - - . X, be a random sample from a continuous distribution with probability density function
F(x) = dem ‏9و۶‎ 6

LetT =X, + ‏.ملا + . . . + ولا‎ Then which of the following is an unbiased estimator 01 ம?

T T 3T
^) =— 8) — = D) —
) 2n ) 30 0 2 ) 30

Let ‏,رلا‎ Xp, . - .X, be a random sample from U(0, 6). Define Xin) = Max {X1,Xp,...X,}. To test
110 : 6 = 60 against H, : 6 = 61, (942 90), consider the test function x) = 1 if 20) > 00 , then
the size and power of the test are respectively Hx) = a if0< Xin) <0

A) (५, 1-0) 8) (o/2,1 - ५)

2 யப ५१ D) 0 ५१