8. Suppose that X₁, X₂, ..., X₂ is a random sample available from a population distributed as theBernoulli with parameter 0.(a) Find the Cramer-Rao lower bound variance for the estimator of 0.(b) Using the invariant property of maximum likelihood estimators,i. Find the estimator of 0² and show whether or not it is unbiased.ii. Find the Cramer-Rao lower bound variance for the estimator of 02 and its absoluteefficiency.

Given that X1, X2, . . ., Xn be a random sample from a population distributed as the Bernoulli with…

Answered: 8. Suppose that X₁, X2, ..., X₂ is a…

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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Let x, x2, ..., Xn be a random sample from a Poisson distribution with parameter 2. Find ML estimator of 2. Also find its variance.
Let X1, X2, X3, and X4 be a random sample of observations from a population with mean μ and variance σ2. Consider the following estimator of μ: �"!= 0.15 X1 + 0.35 X2 + 0.20 X3 + 0.30 X4.What is the variance of � "!
(e) Show that the sample mean of a simple random sample (drawn without replacement from a normal population) is dis- tributed normally with mean u and variance -² (1--=-1). n where N and n are population and sample sizes respectively. 4 In the 1 1 TI
Suppose that a random man's weight from a certain population is M~ Normal (μ = 200, o²49) and a random woman's weight is W ~ Normal( 140, o² = 25). If M and W are independent, what is the variance of the difference between a man's weight and a woman's weight, i.e. Var (M-W)? (a) 340 (b) 24 (c) 140 (d) 200 (e) None of the above
a) & b)
Please answer all bits
i need help with c
Let Y1 and Y2 be independent random variables with unknown mean μ and known variance σ2 =1. Which of the following two estimators of μ has smaller MSE? Justify your answer.
1. Suppose that a variance is thought to be σ² = 3. A random sample of n=25 yields a sample standard deviation of s=2.1. α=0.05. (a) Test the hypothesis that the variance is not equal to 3 by using critical regions. (b) Test the hypothesis using the P-value.
A manufacturing company is interested in buying one of two different kinds of machines for production purposes. The first machine was run for 20 hours. It produces on average of 40 items per hour with variance of 8 items2. The second machine was run for 15 hours. It produces on average 50 items per hour with variance of 10 items2. Assume that the production per hour for each machine is (approximately) normally distributed and there a homogeneity between the populations' variances of the number of items produced by the 2 machines Compute 90% confidence interval for the difference between the two means. What is the tabulated value What is the S.E value What Is the lower and upper bound
A survey of the white and nonwhite population in a local area reveals the following annual trip frequencies to the nearest state park: X̄1 = 4.1 X̄2= 3.1 s21 = 14.3 s22= 12.0 N1= 20 N2= 16 Where the subscript '1' denotes the white population and the dubscript '2' denotes the nonwhite population. (a) assume the variances are equal, and test the null hypothesis that there is no difference between the park-going frequences of whites and nonwhites (d) Associated with the test in part (a), find a 95% confidence interval for the difference in means
Show that the characteristic function of a Gaussian random variable with zero mean and variance o² is (= x (@) = exp -0² w² 2

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