Question: If X is a random variable having the binomial distribution with the parameters n and , show that n X/n (1 X/n)

If X is a random variable having the binomial distribution with the parameters n and θ, show that n ∙ X/n ∙ (1 – X/n) is a biased estimator of the variance of X.

Step by Step Solution

★★★★★

3.44 Rating (157 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

n 11 n1 bia... 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)

583-M-S-P-E (764).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

What is the dealer's average profit per automobile if the profit on each automobile is given by g(X) = X2, where X is a random variable having the density function of Exercise 4.12?

If X is a random variable having a geometric distribution, show that P(X = x + n| X > n) = P(X = x)

With reference to Exercise 6.17, using the fact that the moments of Y about the origin are the corresponding moments of X about the mean, find a3 and a4 for the exponential distribution with the...

If x is a random variable having the binomial distribution with the parameters n and , show that n * x n * ( 1 - x n ) is a biased estimator of the variance of x .

An alternative proof of Theorem 5.2 may be based on the fact that if X 1 , X 2 , . . ., and X n are independent random variables having the same Bernoulli distribution with the parameter ., then Y =...

Let X be a random variable having the binomial distribution with parameters n and p. (i) Show that its probability function f (x), x = 0, 1,, n, can be calculated via the recursive relation with...

ST107 Exercise 7 In this exercise you will practise point estimation by investigating the properties of different estimators. Question 1 involves the estimation of the probability of success, , based...

(a) How does the use of condition codes complicate the implementation of a superscalar processor that supports out-of-order execution? [4 marks] (b) A branch predictor with a high prediction accuracy...

Let X be a random variable having the binomial distribution with parameters n and p for some p (0, 1) and Y be another random variable having the binomial distribution with parameters n and q, where...

Let X be a random variable that follows the binomial distribution with parameters n and p, and denote by Xn the proportion of successes in the n trials. Show that for any positive real number ????...

The thiourea in a 1.455-g sample of organic material was extracted into a dilute H2SO4 solution and titrated with 37.31 mL of 0.009372 M Hg2+ via the reaction Find the percentage of (NH2)2CS (76.12...

Determine, for each of the following, whether it would appear in the current account or capital account section of the U.S. balance of payments accounts and whether it would represent an inflow or an...

Current Attempt in Progress Blossom Company reports net income of $ 9 3 , 2 0 0 in 2 0 2 2 . However, ending inventory was understated $ 9 , 2 0 0 . What is the correct net income for 2 0 2 2 ?...

Governments: a) can play an important role in stabilizing markets; b) can stabilize markets only through austerity policies; c) are never able to stabilize markets; d) none of the above.

Bayess rule was applied to the problem of HIV testing in The American Statistician (Aug. 2008). In North America, the probability of a person having HIV is .008. A test for HIV yields either a...

Nondestructive evaluation (NDE) describes methods that quantitatively characterize materials, tissues, and structures by noninvasive means, such as X-ray computed tomography, ultrasonics, and...

The local area network (LAN) for the College of Business computing system at a large university is temporarily shut down for repairs. Previous shutdowns have been due to hardware failure, software...

On February 18th, Ohio State announced that it had entered into exclusive contracts with two companies (company ABC and XYZ) to manufacture all universityrelated apparel. No additional news regarding...

Please provide detailed solutions. Thank you! 1458 As a measure of productivity, Verizon Wireless records the number of customers each of its retail employees activates weekly. An activation is...

A publicly-held corporation has recently reported the following financial statements as of 31/12/2020. Balance sheet Assets Liabilities and equity Short-term assets 3,000,000 Debt 12,000,000...