If X 1 ,X 2 , , X n is a random sample from a distribution having pdf of the form f(x ) x 1 , 0 x 1, zero elsewhere, show that a best critical region for testing H 0 1 against H 1 2 is C (x 1 , x 2 , , x n ) c n i 1 x i

Question: If X 1 ,X 2 , . . . , X n is a random sample from a distribution having pdf of the form f(x;

If X₁,X₂, . . . , X_n is a random sample from a distribution having pdf of the form f(x; θ) = θx^θ−1, 0 < x < 1, zero elsewhere, show that a best critical region for testing H₀ : θ = 1 against H₁ : θ = 2 is C = {(x₁, x₂, . . . , x_n) : c ≤ Пⁿ_i=1 x_i}.

Step by Step Solution

★★★★★

3.29 Rating (152 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Proof We set C x1 x2 xn c ni1 xi Choose ni1 to be as small as possible while C has at least a finite ... 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

Students Have Also Explored These Related Statistical Techniques in Business Questions!

If X 1 ,X 2 , . . . , X n is a random sample from a distribution that has a pdf which is a regular case of the exponential class, show that the pdf of Y 1 = n 1 K(X i ) is of the form f Y 1 (y 1 ; )...

If X 1 ,X 2 , . . . , X n is a random sample from a distribution with pdf show that Y = 2 X is an unbiased estimator of and determine its efficiency. f(x; 0) = { 303 (x+0)4 0 0

need full answer to attached question 3. Let X 1, X 2, . . . , X n be a random sample from a population with probability density function (26 i 1) 6 1 7 I9 fx(59;9) = (:6) 5'3 Find a Maximum...

STA5326 - Mathematical Statistics - II Homework # 3 1. If X 1 , X 2 ,..., X n is a random sample of size n from N ( , 2 ), , show that n n n 2 2 X j , X j or X , X j = = j 1 j 1 =j 1 is a sufficient...

\f 1 Let X 1 , X 2 ,....., X n is a random sample from a normal distribution with mean and variance 02 known. Then probabilily density function 1 x i 2 0 1 f xi 2 e , xi , 0, 0 2 By def, Likelihood...

Please help with this question. Please provide all steps and calculations. Please don't use answers from other websites, I looked at them and didn't understand them. Thank you Problem 7 Let X 1, X 2,...

Recall: k) In addition to many other wonderful services it provides, CourseCheggHero benets nancially from its customers' inability and/ or unwillingness to do their homework. Suppose that the time...

The pdf of an exponential distribution with mean is: f(x|) = 1 exp (x/), x > 0, > 0. Let X1, . . . , Xn be a random sample from this pdf. a) Derive the MLE of . It is required to justify that your...

class Student: def __init__(self, my_id): self.id = my_id Suppose student1 is a Student object. Which of the following statements displays the value of the instance variable id? A. print(student1.id)...

can mins/ For the one said the) 13), use the summary statistics of a sample S that are mentioned below to solve the questions. Round final answers to 4 decimal places if needed. n = 21 x = 33.2 y =...

On January 1, 2016, Seaside Condo Association issued bonds with a face value of $250,000, a stated rate of interest of 8 percent, and a 10-year term to maturity. Interest is payable in cash on...

Why do noble gases have comparatively large atomic sizes?

In 2 0 2 4 , Gates Corp. started a construction job with a total contract price of $ 2 1 , 0 0 0 , 0 0 0 . The job was completed on December 1 5 , 2 0 2 5 . Additional data are as follows: Actual...

Describe how organizations combine incentive plans in a balanced scorecard. page 546

Below is a partial statistical summary of the first twenty-four Super Bowls (33). Of particular interest to advertisers is the network share that each game garnered. Can those shares be considered a...

In the next column are the lengths (in mm) of furniture dowels recorded as part of an ongoing quality control program. Listed are the measurements made on thirty samples (each of size 4) taken in...

Listed below are forty ordered observations generated by Minitabs RANDOM command that presumably represent a normal distribution with = 5 and = 2. Can the sample be considered random with respect...

RST, Inc. has total assets of $9,900,000 and a total asset turnover of 2.49 times. Assume the return on assets is 11 percent. What is its profit margin? (Do not round intermediate calculations and...

a) The financial manager should identify surplus assets and dispose of them'. Why? (b) Marcon Limited is considering purchasing a new truck which is expected to save labour on an existing project....

1) Jane has a margin account and deposits $80,000 into it. Assume that the prevailing margin requirement is 50%, interest and commissions are ignored and and Alpha Inc. is selling for $47.50a share....