Consider a random sample of size n. Let each element of therandom sample have mean O and variance 1. Let the sample meanestimator be given byXN = ΣΧ . The variance of X is equal to1/NCannot be determined.0 1

Answered: Consider a random sample of size n. Let…

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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2. Suppose that X1, X2, X3 and X4, are independent and identically distributed with a mean of 2.5 and a standard deviation of 0.6. Find the mean and standard deviation for variables Y and W defined below. Let Y= 4X1 а. b. Let W= Xi + X2 + X3 + X4
Consider an estimator of μ: W= 1/6 Y1+1/16Y2+1/4Y3+1/8Y4+1/2Y5 This is an example of a weighted average of the Yi's. Show that W is also an unbiased estimator of μ. Find the variance of W.
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Let X denote the sample average for a random sample with mean uu and variance 02. Consider the following estimator for u: W=n+2/n+1°X Is W as consistent estimator of u? a. Yes b. No c. It depends
Compute for the variance and standard deviation of the population
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Suppose that X₁,..., Xn are i.i.d. from a normal population with mean μ and variance o². Calculate the expected value and the variance of the sample mean X and find the distribution of √n(X − µ).
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Let X-1: correct, X=0 : wrong And P= Pr(X=1)=2/5 What is the variance? .32 O.6 O .4
Let G and H be two independent unbiased estimators of 0. Assume that the variance of G is two times the variance of H. Find the constants a andb so that aG + bH is an unbiased estimator with the smallest possible variance for such a linear combination.
Q1.2 Mean of X A medical practice collects data on its patients with respect to several personal habits. The following table gives the distribution of the number of alcoholic drinks consumed per day in that population of patients. X = # of drinks per day Probability Save Answer Q1.3 Variance of X X = # of drinks per day Probability 0 0.38 Find the mean for this random variable, that is find ux. Show your work in the space below. Save Answer A medical practice collects data on its patients with respect to several personal habits. The following table gives the distribution of the number of alcoholic drinks consumed per day in that population of patients. 0 0.38 Q1.4 Standard Deviation of X X = # of drinks per day Probability 1 0.32 0 0.38 1 0.32 2 0.25 Find the variance for this random variable, that is find (ox)². Only show the first and last term of the work required. 1 2 0.25 A medical practice collects data on its patients with respect to several personal habits. The following table…
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Consider a random sample of size n. Let each element of the random sample have mean 0 and variance 1. Let the sample mean estimator be given by N Χ ÎN = Σ²1 Xi i=1 XN N The variance of XN is equal to O 1/N O Cannot be determined. 01