Let X1, , Xn be a random sample from an infinite population with finite variance 2 Define Show that S '2 is a biased estimator for 2, and that the bias of S '2 is 2 n Thus, S '2 is negatively biased, and so on average underestimates the variance Note that S '2 is the MLE of 2 O (, )

Question: Let X1, . . ., Xn be a random sample from an infinite population with finite variance 2. Define Show that S'2 is a biased

Let X1, . . ., Xn be a random sample from an infinite population with finite variance Ïƒ2. Define

Show that S'2 is a biased estimator for Ïƒ2, and that the bias of S'2 is €“ Ïƒ2 / n. Thus, S'2 is negatively biased, and so on average underestimates the variance. Note that S'2 is the MLE of Ïƒ2.

O (, -).

Step by Step Solution

★★★★★

3.49 Rating (159 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Using a similar method to t... View full answer

Question Has Been Solved by an Expert!

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

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

610-M-S-O-T-S-E (843).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Let X1, X2,..., Xn be a random sample from an exponential distribution with parameter . Then it can be shown that 2Xi has a chi-squared distribution with v = 2n (by first showing that 2Xi has a...

Let X1,..., Xn be a random sample from a n(Î¼, Ï2) population, where both Î¼ and Ï2 are unknown. Each of the following methods of finding confidence intervals for...

Let X1,..., Xn be a random sample from a n(Î¸, Ï2) population. Consider testing H0: Î¸ Î¸0. (a) If Ï2 is known, show that the test that rejects Ho when...

10-33. Let X1, . . . ,Xn represent a random sample taken from a population with meanand variance 2. Let Xn = 1n ni =1 Xi and S2n = 1 (n1) ni =1(XiX)2 depict sequences of estimators for and 2,...

59. Let X1, . . . , Xn be a random sample from a normal distribution with both m and s unknown. An unbiased estimator of u P(X c) based on the jointly suf cient statistics is desired. Let and . Then...

I need help with finding the MLE as well as part ii and iii please Let X1, . .., Xn be a random sample from a distribution with probability density func- tion 1 fx (2; a) (k-1),akxk-le ar for x > 0...

Let X1, ...,Xn be a random sample from a Bernoulli distribution with an unknown p. Show that the variance of any unbiased estimator of (1 p)2 must be at least 4p(1 p)3/n.

Can you help me with this question. It is taken from Statistical Inference, Berger and Casella. ulle estimators in the previous two exercises. itsmoseysuit el an To allMe 7.22 This exercise will...

Hi, it's me again Thanks for helping me with the answer last time d u 1. (a) Let Y1, Y2, ..., Yn be a random sample from a Bernoulli (p) distribution (i.e. Binomial(1, p)). Show ELI K is a minimal...

Exercise 4. (20 points) Let X1...., Xn be a random sample of size n from an infinite population and assume X1 d= a + 2Y with a > 0 unknown and Y having an exponential distibution with parameter = 2....

Noda plc (Noda) is a large company which your firm has just accepted as a new client. You are the audit manager for Noda and are planning the audit for the year ended 31 December 20XY. The principal...

Described below are potential financial statement misstatements that are encountered by auditors in the audit of inventory and cost of goods sold. a. Management of a chain of discount department...

Under what circumstances is it appropriate to change Outback Outfitters' Sydney plant from a profit centre to an investment centre?

Some business marketers organize their sales force around products; others are market centered. What factors must be considered in selecting the most appropriate organizational arrangement for the...

Order Statistics. Let X1, X2, , Xn be a random sample of size n from X, a random variable having distribution function F(x). Rank the elements in order of increasing numerical magnitude, resulting in...

Continuation of Exercise 7-65. Let X1, X2, , Xn be a random sample of a Bernoulli random variable with parameter p. Show that Use the results of Exercise 7-65.

Continuation of Exercise 7-65. Let X1, X2, , Xn be a random sample of a normal random variable with mean and variance 2. Using the results of Exercise 7-65, derive the probability density functions...

Haskell Corp. is comparing two different capital structures. Plan I would result in 18,000 shares of stock and $95,000 in debt. Plan II would result in 14,000 shares of stock and $190,000 in debt....

In java make a program that reads within a txt file any numbers 0-9 and any word or any letter from a range of A-Z upper and lowercase

Question 3 3.33 pts Suppose a bank has a negative GAP and management believes interest rates will rise over the next three years. Should this bank buy an interest rate cap or floor to hedge their...