1 answer

PROBLEM 3 Let X1, X2, ..., Xn be a random sample from the following distribution -...

Question:

PROBLEM 3 Let X1, X2, ..., Xn be a random sample from the following distribution - 5) +1 if 0 <r <1 fx(2) = 10 0. 0.w.. where

PROBLEM 3 Let X1, X2, ..., Xn be a random sample from the following distribution - 5) +1 if 0 <r <1 fx(2) = 10 0. 0.w.. where @ € (-2, 2) is an unknown parameter. We define the estimate ēn as: ô, = 12X – 6 to estimate . (a) Is ên an unbiased estimator of e? (b) Is Ôn a consistent estimator of e?

Answers

Here Be [-2, 2 (F-6) E (n)E 12 E()-6 E(R) tamdom, tha arte imdupendct E(x)wislen, 6(x) fx (i) d dri zidnt 2 D 3 2 3 2 x2- 4-3 2 12 + 2 /2 +(1) n 2 12 E (o)12 12 2 Au that E( we o estmmator of By chebyshevs Tneualit PE the Vos (n) E2 Vore (on) E ()E() E -j 12 x 6 6e (r) Vax ()+ Eg) ar() (ii) = as E(K)-E are randsu 1e. they arLe ndspendnt E (x) 2 tz) dx 2 di i d t dxi i 2 2 3 6 (6-9 3 12Vase ) n 2 i21 [2 2 44 (#-X *-166 82 12 144 11.a (x) ()Ex) Var 2 74니 12 (유+놀 2 2 [44 Q2 +2x xL /u4 2 2 12-e2 2 44 12 -13 Sl12- = १५५ * 144 72 +36 2 34 + 126 - 12-2 +34 12 +02 Var (n 12-2 n 12-62 that is a cenristent We Knous estimator tohem twe get

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