nExample 17-21. Show that X = £ X¡ / n, in random sampling fromi=1- exp (-x/0), 0

Answered: Image /qna-images/answer/53efaf99-75c8-4550-9e25-0f4fdfa1ebf8.jpg

Answered: Example 17-21. Show that X = 2 X¡ / n,…

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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7. If x1, X2 and x3 three variates measured from their are respective means as origin and if e¡ is the expected value of x1 for given values of x2 and x3 from the linear regression of x, on x2 and x3, prove that cov (x1, e¡) = var (e¡) = var (x1) – var (x; - ei). ||
6) Consider the random variable Zn = cos (2 * T : * Yn/n) where Yn is binomial(n,p) a. What is its asymptotic variance for arbitrary p as n increases b. What happens at p=1/2
Example 11: Find the maximum likelihood estimator for p when f (x ; p) = p* (1 – p)'- for x = 0, 1.
2. A random sample X₁, X2, X3 of size 3 is drawn from a population with mean and variance o2. Let 1 3 Đi (Xi+X+X3) - (X₁ + X2 + X3), (3X₁ — X₂ +2X3). - 4 (a) Show that ₁ and ₂ are both unbiased estimators of the population 2 = mean . (b) Compute the variance of ₁ and 2. (c) Which estimator would you use? Explain your answer.
3. Consider two random variables X₁ and X2 whose joint pdf is given by for x₁0, x2 > 0, x₁ + x2 < 2, { Find the pdf of Y = X₂ - X₁. f(x1, x₂) = NIT otherwise.
Suppose that Y₁, Y₂, ..., Ym is a random sample of size m from Gamma (a = 3, B = 0), where 0 is not known. Check whether or not the maximum likelihood estimator Ô is a minimum variance unbiased estimator of the parameter 8.
2
6
Consider a set of data x1, x2, n n i=1 ..., n taken from a population with mean µ. - Show that (x-μ)² = Σ(x₂ − x)² + n(x − µ)². i=1
4.
1. If X,X2, .,X, forms a random sample of size n from a population with pdf f(x; 0,8) = for x>0 elsewhere Find estimators for 8 and 0 by the method of moments.
Example 3.17 Let X be a discrete random variable with range Rx = {0, 7, 5, ,"}, such that Px(0) = Px(;) = Px(5) = Px() = Px(x) = . Find Esin(X).

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Example 17-21. Show that X = 2 X¡ / n, in random sampling from i= 1 %3D exp (-x/θ , 0 < x < ~ f(x, 0) = %3D 0, otherwise where 0< 0< o, is an MVB estimator of 0 and has variance In.