For some 0 € (0, 1), define the density on the interval (0, 2) :Vx € (0, 1],00 Vx € (1,2).f (x|0) = { ₁-1-(a) Verify that f(x0) is a probability density function and draw a picture of it for 0 = ³1.Suppose X₁,.,..., Xn is a random sample from f(x|0).(b) Compute the method of moments estimate for 0.(c) Is the estimator in (b) unbiased? Justify your answer.

Given the probability density function of random variable X:

Answered: For some € (0, 1), define the density…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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8)Let X1, X2, ..., Xn be a sample of n units from a population with a probability density function f (x I θ)=θxθ-1 , 0<x<1, θ>0 . According to this: Find the joint probability density function of the order statistics X(2), X(4), X(6) for n = 7.
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c) Let Y₁, Y₂,..., Yn be a random sample whose probability density function is given by f(v:B)= 684 - fa 00 0, elsewhere 200 200 200 and suppose that n = 200, y = 20, y = 100, y = 250 and $ = 0.025. i=1 i) Derive the standard error of ß, se(B) = 0.0009, using MLE approach. ii) Find an approximate 95% Confidence interval for B.
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