Let X1, X2, , Xn be a random sample from an exponential distribution with mean Icirc cedil Show that the likelihood ratio test of H0 Icirc cedil Icirc cedil 0 against H1 Icirc cedil Icirc cedil 0 has a critical region of the form How would you modify this test so that chi square tables can be used easily E 1xi c1 or Ef 1ti z c2

Question: Let X1, X2, ... , Xn be a random sample from an exponential distribution with mean Î¸. Show that the likelihood ratio test of H0:

Let X1, X2, ... , Xn be a random sample from an exponential with mean Î¸. Show that the likelihood ratio test of H0: Î¸ = Î¸0 against H1: Î¸ ‰ Î¸0 has a critical region of the form

How would you modify this test so that chi-square tables can be used easily?

E-1xi < c1 or Ef-1ti z c2.

Step by Step Solution

★★★★★

3.37 Rating (153 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

In Thus Plotting as a function of w x0 we see that 0 when x0 0 it has a ... 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)

579-M-S-H-T (3071).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 . Show that the random variable 20(EX,)~x*(2n).

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 sample from an exponential distribution with parameter y. Show that an LRT of H0:P = 0 versus Ha: 6 = 0 rejects the null hypothesis if 2m or

I am interested in purchasing investment property in downtown Atlanta. The one comparable property sold at $10 million last year and was 15,000 square feet. The property I'm interested in is also...

Question 1 Let X1, X2, .., Xn be a random sample drawn from a distribution with probability density function f (x; 0) = 7 ( 1 + x ) 0+ 1, 0 0 is an unknown parameter. (a) Show that Y, = In(1 + X;)...

4 Mathematics 341/686 December 8, 2015 1. Let X1 , X2 , . . . , Xn be a random sample from N (1 , 2 ) and let Y1 , Y2 , . . . , Yn be a random sample from N (2 , 2 ) and 2 is known. (a) Find the...

GU4204/GR5204 - Statistical Inference Final Exam - Fall 2016 December 20 Please show your work in all the problems to get full credit. Time: 90 min Name: - UNI: 1. Suppose X1 , X2 , ..., Xn is a...

Let X1, X2, . . . , Xn be a random sample of size n from the normal distribution N(, 02), where 02 is known but is unknown. (a) Find the likelihood ratio test for H0: = 0 against H1: 0. Show that...

Assume that the weight X in ounces of a 10- ounce box of cornflakes is N(, 0.03). Let X1, X2, . . . , Xn be a random sample from this distribution. (a) To test the hypothesis H0: 10.35 against the...

Let X 1 ,X 2 , . . . , X n be a random sample from the normal distribution N(,1). Show that the likelihood ratio principle for testing H 0 : = ' where ' is specified, against H 1 : ' leads to the...

Impact of covid-19 in share market: an overview of Bangladesh?

Draw a vertical line through a normal distribution for each of the following z-score locations. Determine whether the tail is on the right or left side of the line and find the proportion in the...

6. At the q3 level of output, A. AFC = $d2 $d1. B. MC = $d2. C. TVC = $d2. D. ATC = $d3. E. AFC = $d3 $d2.

Use the data in APPROVAL to answer the following questions. The data set consists of 78 months of data during the presidency of George W. Bush. (The data end in July 2007, before Bush left office.)...

Based on past experience, the number of customers who arrive at a local gasoline station during the noon hour to purchase fuel is best described by the probability distribution given in the file...

Let X be the number of defective items found by a quality inspector in a random batch of 15 items from a particular manufacturing process. The probability distribution of X is provided in the file...

The probability distribution for the number of job applications processed at a small employment agency during a typical week is given in the file S04_43.xlsx. a. Assuming that it takes the agencys...

Please show steps and explanations. Counting passwords: Consider the following sets of characters: Letters: L = {a, b, c, d, e, f, g. h, i, i, j. k. l, m, n, 0. p, q, r, S. t, u, v. w, x, y, z}(26...

Question: Formulate the optimization problem . Specify the decision variables, the objective function, and the constraints. The objective function and the constraints must be based on the input...

May someone help me with this and the formula you would use in a calculator. Will thumbs up Sales for Hanebury Corporation's just-ended year were \$14 million. Sales were \$7 million 5 years earlier....