Let X1, , Xn be a random sample from a n(0, 2X), and let Y1, , Ym be a random sample from a n(0, 2Y), independent of the As Define 2Y 2X a Find the level a LRT of H0 0 versus H1 0 b Express the rejection region of the LRT of part (a) in terms of an F random variable c Find a 1 confidence interval for

Question: Let X1,..., Xn be a random sample from a n(0, 2X), and let Y1,..., Ym be a random sample from a n(0, 2Y), independent of

Let X1,..., Xn be a random sample from a n(0, σ2X), and let Y1,..., Ym be a random sample from a n(0, σ2Y), independent of the As. Define λ = σ2Y/ σ2X.
a. Find the level a LRT of H0: λ = λ0 versus H1: λ ≠ λ0.
b. Express the rejection region of the LRT of part (a) in terms of an F random variable.
c. Find a 1 - α confidence interval for λ.

Step by Step Solution

★★★★★

3.33 Rating (168 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a The unrestricted MLEs of 2 X and 2 Y are 2 X X 2 i n and 2 Y Y 2 i m as usual Under the restrictio... 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)

941-M-S-H-T (5450).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Let X1, . . ., Xn be a random sample from an exponential population with parameter . Let Y1, . . ., Yn be the ordered random variables. (a) Show that the sampling distributions of Y1 and Yn are given...

Let X1, . . ., Xn be a random sample from a geometric distribution with pmf Show that pi = P (X = i) = pqi-l , i-1,2, ,0

Let X1, . . ., Xn be a random sample from the truncated exponential distribution with pdf Show that the MLE of y is min (Xi;). f(x) 0, otherwise

Let X1, . . ., Xn be a random sample from an N (1, 2) population and Y1, . . ., Yn be an independent random sample from an N (2, 2) distribution where 2 is assumed to be known. Construct a (1 ) 100%...

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....

Let X1,..., Xn be a random sample from a n(, 2) population. Consider testing H0: 0 versus H1 : > 0. Let m denote the sample mean of the first m observations, X1,... ,Xm, for m = l,...,n. If 0 +...

9.4 Let X1, ..., Xn be a random sample from a n(0, x ), and let Y1, . .., Ym be a random sample from a n(0, op ), independent of the Xs. Define A = ov /ox. (a) Find the level a LRT of Ho: A = do...

Mathematics 341/686 Assignment 2 Due Oct 26, 2015 in Class 1. Let X1 , . . . , Xn be a random sample from N (, 1). Assume a uniform (0, ) prior distribution for . (a) Find the posterior distribution...

2. Suppose that X1, ..., Xn are a random sample of size n with a Beta(/, 1) pdf and Y1, . .., Ym are an i.i.d sample of size m with a Beta(0, 1) density. Also assume that the X's are independent of...

(a) Let X1, , Xn be a random sample with finite variance. T 1. (4 points) True/False. Please read the statements carefully, as no partial credit will be given. (a) Let X1, . .. , Xn be a random...

"One can judge the presence or absence of discrimination by looking at the proportion of the population in different occupations." Does such information help? Does it suffice? Consider each of the...

kdd.ics.uci.edu/databases/covertype/covertype.data.html (Blackard, 1998). They consist of a subset of the measurements from 581,012 3030m cells from Region 2 of the U.S. Forest Service Resource...

10. Why are brand names and trademarks not amortized?

If the total marks are increased to 300, compute the new table showing the combined upgraded marks.

A college infirmary conducted an experiment to determine the degree of relief provided by three cough remedies. Each cough remedy was tried on 50 students and the following data recorded. Test the...

To determine current attitudes about prayers in public schools, a survey was conducted in 4 Virginia counties. The following table gives the attitudes of 200 parents from Craig County, 150 parents...

According to a Johns Hopkins University study published in the American Journal of Public Health, widows live longer than widowers. Consider the following survival data collected on 100 widows and...

You work for a nuclear research laboratory that is contemplating leasing a diagnostic scanner ( leasing is a common practice with expensive, high - tech equipment ) . The scanner costs $ 4 , 9 0 0 ,...

-You have contacted a number of car dealerships to determine the best interest rate on a new automobile loan. A Ford dealership has quoted you a 5-year, 10% loan in the amount of $35,000 that will...

Harry, Tamara, and Lana were partners under a written agreement made in February that the partnership should continue for ten years. During the same year, Lana, being indebted to Jones, sold and...