Question: Let 5'2 be the sample variance of a random sample drawn from a N (,u, 02) distribution. Show that the constant c = (n 1)

Let 5'2 be the sample variance of a random sample drawn from a N (,u, 02) distribution. Show that the constant c = (n 1) / (n + 1) minimizes E[(c.5'2 02m. Hence, the estimator (n + 1)'1 221:1(Xi X)2 of 02 minimizes the mean square error among estimators of the form (:82. [10 marks]

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

ses . .. (From 1617 $2 past paper)Let X1, . . . , X13 be a random sample drawn independently from N (u, 02). Let s2 be the sample variance. Suppose 02 = 5. Find the constant 1' such that P(82

Let S^2 be the sample variance of a random sample drawn from a N(,^2) distribution. Show that the constant c = (n 1)/(n + 1) minimizes E[(cS^2 ^2)^2]. Hence, the estimator (n + 1)^-1 x sum (Xi X)^2...

Solution: Consider the population described by the probability distribution below.[7.5 Marks]? X 3 5 7 P(X) 0.1 0.7 02 a. Find of. b. Find the sampling distribution of the sample variance S?for a...

2. 3. 4. 5. 6. 7. The Bem Sex Role Inventory (BSRI) provides independent assessments of masculinity and femininity in terms of the respondent's self-reported possession of socially desirable,...

Problem 1. Problem 2. Problem 3. Problem 4. 1. (10 points) Let X; for i =1,2,..., n be independent and identically distributed random variables with mean u > 0 and standard deviation o > 0. When we...

uiz - II 1. Find the sample space that describes all two-child families according to the genders of the children with respect to birth order. (a) {b, g} (b) {bb, gb} (c) {bb, gb, bg, gg} (d) {bb, gb,...

1 The mean height of the women in a large population is 1.671m while the mean height of the men in the population is 1.758m. The mean height of all the members of the population is 1.712m. Calculate...

For each given situation, determine/indicate the probability distribution model that fits the random variable being described. 9. . Suppose that the average number of telephone calls arnving at the...

2. Suppose that X is the number of observed "successes " in a sample of n observations where p is the probability of success on each observation a. Show that p = X is an unbiased estimator for p. b....

The following information pertains to Torasic Companys budgeted income statement for the month of June 2011: Sales (1,200 units at $250) $300,000 Variable cost 150,000 Contribution margin $150,000...

What good is economic theory if it cant predict the behavior of a specific individual?

1 pts Question 1 Which statement is true about period and product costs? Period cost is necessary to support the existence of the organization itself rather than the actual delivery of a service....

The political landscape in Britain Within this paradox democracy is triumphant throughout the world with new waves of democracy occurring in Eastern Europe, Latin America and Asia; but in contrast...

1. Explain the following statements: a) Objective reality is always subjectively interpreted. b) What we know depends on whom we got to know it from.

4. Give examples from your everyday life where the process affects the result, but where the result also affects the process.

6. Give examples of circular patterns in a communication situation that you have participated in, where element A affects B, and B affects A.