24. For arandom sample of size n from a population of size N, consider the followingas an estimate of :where the ci are fixed numbers and Xi, , X, is the sample.a. Find a condition on the ci such that the estimate is unbiased.b. Show that the choice of c, that minimizes the variances of the estimate subjectto this condition is c1/n, wherei

Given for a random sample of size n the estimate of mean is given below.It is given that the…

Answered: 24. For arandom sample of size n from 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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given normally distributed sample x=12 and s=3, use the Empirical Rule determine the upper and lower bounds to contain approximately 95% of your data
1. Suppose X1,X2,...,Xn is a random sample of size n > 5 that comes from a distribution with E[X] = μand V ar(X) = σ2. Consider the following two estimators where ̄X is the sample mean:ˆμ1 = (n −3/n) ̄Xˆμ2 = 0.95 ̄X(a) Which of the estimators is an unbiased estimator for μ?(b) Which is the variance of the two estimators?(c) Given the properties above, which one would you prefer? Is there another property that wouldinfluence your decision? Explain.
For which of the following conditions is it not appropriate to assume that the sampling distribution of the sample mean is approximately normal? A. A random sample of 8 taken from a normally distributed population B. A random sample of 50 taken from a normally distributed population C. A random sample of 10 taken from a population distribution that is skewed to the right D. A random sample of 75 taken from a population distribution that is skewed to the left E. A random sample of 100 taken from a population that is uniform
A chemical supply company currently has in stock 100 lb of a certain chemical, which it sells to customers in 4-lb batches. Let X = the number of batches ordered by a randomly chosen customer, and suppose that X has the following pmf. x 1 2 3 4 p(x) 0.3 0.5 0.1 0.1 (a) Compute E(X) and V(X). (b) Compute the expected number of pounds left after the next customer's order is shipped and the variance of the number of pounds left. [Hint: The number of pounds left is a linear function of X.]
If X1, X2, and X3 constitute a random sample of sizen = 3 from a normal population with the mean μ and thevariance σ2, find the efficiency of X1 + 2X2 + X34relative toX1 + X2 + X33as estimates of μ.
Apply the Slovin’s formula to calculate the minimum sample size for a population of 3,658 when e = 0.10.
Suppose that a random sample of size 1 is to be taken from a finite population of size N. a. How many possible samples are there?b. Identify the relationship between the possible sample means and the possible observations of the variable under consideration.c. What is the difference between taking a random sample of size 1 from a population and selecting a member at random from the population?
If We can assert with 95% that the maximum error is 0.05 and p= 0.2 ,find the sample size...
The number of contaminating particles on a silicon waferprior to a certain rinsing process was determined for eachwafer in a sample of size 100, resulting in the followingfrequencies:Number of particles 0 1 2 3 4 5 6 7Frequency 1 2 3 12 11 15 18 10Number of particles 8 9 10 11 12 13 14Frequency 12 4 5 3 1 2 1a. What proportion of the sampled wafers had at leastone particle? At least five particles?b. What proportion of the sampled wafers had betweenfive and ten particles, inclusive? Strictly between fiveand ten particles?c. Draw a histogram using relative frequency on thevertical axis. How would you describe the shape of thehistogram?
2) Let G and H be two independent unbiased estimators of θ. Assume that the variance of G is two times the variance of H. Find the constants a and b so that aG + bH is an unbiased estimator with the smallest possible variance for such a linear combination.
Let X1,...,Xn be an iid sample from f(x | θ) = θ xθ−1, 0 < x < 1, where the parameter θ is positive. Find the MLE and MOM estimators for θ
Let X1, . . . , Xn be an iid sample from f(x | θ) = θxθ−1 , 0 < x < 1, where the parameter θ is positive. Find the MLE and MOM estimators for θ.

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