If X1, X2, , Xn and Y1, Y2, , Ym are independent random samples from normal distributions with the same 2, prove that their pooled sample variance, s2p, is an unbiased estimator for 2 ...

If X1, X2, . . . , Xn and Y1, Y2, . . . , Ym are

Question:

If X1, X2, . . . , Xn and Y1, Y2, . . . , Ym are independent random samples from normal distributions with the same σ2, prove that their pooled sample variance, s2p, is an unbiased estimator for σ2.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Introduction To Mathematical Statistics And Its Applications

ISBN: 9780321693945

5th Edition

Authors: Richard J. Larsen, Morris L. Marx

See More Books

Question Posted: Dec 20, 2015 03:42 AM

See More Questions

If X1, X2, . . . , Xn constitute a random sample of size n from a geometric population, show that Y = X1 + X2 + + Xn is a sufficient estimator of the parameter .
(a) The numbers x1, x2, . . . , xn and y1, y2, . . . , yn are random observations from the same exponential distribution. (b) The average of x1, x2, . . . , xn is equal to the average of y1, y2, . ....
Suppose that X1, X2, . . . , Xn and Y1, Y2, . . . , Ym are independent random samples from normal distributions with means X and Y and known standard deviations X and Y, respectively. Derive a...
The par yield curve for U.S. Treasury bonds is currently flat across all maturities at 5.50 percent. You have observed following "paired" transaction by your bond portfolio manager: Bond G H...
A health teacher wishes to do research on the weight of college students. She obtains the weights for all the students in her 9 a.m. class by looking at their drivers licenses or state IDs. The...
Trade Restriction Effects on Exchange Rates. Assume that the Japanese government relaxes its controls on imports by Japanese companies. Other things being equal, how should this affect the (a) U.S....
In a trial of a single cylinder oil engine, the following observations were made : Calculate (a) Brake power (b) BSFC (c) Brake thermal efficiency Oil consumption = = 10 kg/h
Jameson Company produces paper towels. The company has established the following direct materials and direct labor standards for one case of paper towels: Paper pulp (3 lbs. @ $0.40)......... $ 1.20...
Examine the principles of non-Newtonian fluid dynamics, discussing the unique rheological properties of non-Newtonian fluids, the challenges in modeling their behavior, and the practical applications...
Proud Corporation acquired 80 percent of Stergis Companys voting stock on January 1, 20X3, at underlying book value. The fair value of the noncontrolling interest was equal to 20 percent of the book...
Prove that the Z ratio given in Equation 9.2.1 has a standard normal distribution.
Let X1, X2, . . . , Xn and Y1, Y2, . . . , Ym be independent random samples drawn from normal distributions with means X and Y, respectively, and with the same known variance 2.Use the generalized...
Decide whether each function whose graph is shown is the graph of a cubic (third degree) or quartic (fourth-degree) function. 1. (a) (b) 2. (a) (b) Match each equation with the correct graph among...
Assume that the City of Coyote has produced its financial statements for December 31, 2024, and the year then ended. The city's general fund was only used to monitor education and parks. Its capital...
1. Why are Us Treasury securities are referred to as Risk free rate of return? 2. Know what the slope of yeild curve can tell us about the economy in the future 3. what the slope of yeild can tell us...
You have 0.5 meters of rope. you cut off 2 tenths of a meter and 5 hundredths of a meter off the rope. how long is the rope now?
A virtual image is produced by an object 2.00 m away from a concave mirror with a focal length of 2.15 m away. What is the magnification of the image?
3. If the Federal Reserve sells bonds: Bank reserves and bank liabilities fall as bondholders reduce their checking accounts by writing checks for the bonds Bank reserves and bank liabilities rise as...
Evaluate the definite integral. Use a graphing utility to verify your result. Jo x arcsin x dx
Selected condensed data taken from a recent statement of financial position of Morino Ltd. are as follows. MORINO LTD. Statement of Financial Position (partial) Other current assets...
Suppose X has an exponential distribution with mean equal to 10.Determine following: (a) P(X > 10) (b) P(X > 20) (c) P(X > 30)
Suppose the counts recorded by a Geiger counter follow a Poisson process with an average of two counts per minute. (a) What is the probability that there are no counts in a 30- second interval? (b)...
Suppose that the logons to a computer network follow a Poisson process with an average of 3 counts per minute. (a) What is the mean time between counts? (b) What is the standard deviation of the time...
An investor put 60 percent of his money into a risky asset offering a 10 percent return with a standard deviation of return of 8 percent, and he put the balance of his risk-free asset offering 5...
There is a bonus with the following characteristics: nominal value $98.650.000 annual coupon rate 4.5% term 5 years, tir 6.5% A) Calculate the price of the bond assuming it is zero coupon B)...
Ida Company produces a handcrafted musical Instrument called a gamelan that Is similar to a xylophone. The gamelans are sold for $949. Selected data for the company's operations last year follow:...

If X1, X2, . . . , Xn and Y1, Y2, . . . , Ym are

Question:

Step by Step Answer:

It follows from E...View the full answer

Introduction To Mathematical Statistics And Its Applications

Students also viewed these Statistics questions