Let X1,..., Xn be independent with pdfs fx, (x|) = ei-x I(i,)(x). Prove that T = mini(Xi/i)

Question:

Let X1,..., Xn be independent with pdfs fx, (x|θ) = eiθ-x I(iθ,∞)(x). Prove that T = mini(Xi/i) is a sufficient statistic for 6. Based on T, find the 1 - α confidence interval for θ of the form [T + a, T + b] which is of minimum length.

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

Step by Step Answer:

Related Book For book-img-for-question

Statistical Inference

ISBN: 978-0534243128

2nd edition

Authors: George Casella, Roger L. Berger

See More Books

Question Posted: May 26, 2016 05:29 AM

See More Questions

Let X1, . . ., Xn be independent and identically distributed random variables with pdf f(x) = (1 / )e x/, x > 0, y > 0. Find the pdf of -.
Let X1, . . ., Xn be independent discrete random variables identically distributed as Using CTL, find the approximate value of P X-bar100 > 2), where 0.2, 0,1,2,3,4, 0, otherwise x100 = (1 /100)glx,
Let X1, . . . ,Xn be independent and identically distributed random variables. Find E[X1|X1 + + Xn = x]
Access various employment Web sites (for example, www.monster.com and www.dice.com ) and find several job descriptions for a database administrator. Are the job descriptions similar? What are the...
Why would an investor find convertible preferred stock attractive?
A granular material is observed being dumped from a conveyor belt. It forms a conical pile with about the same slope angle, 1.8 horizontal to 1 vertical. What is the angle of internal friction of...
Match the following concepts: goal, process, function, scenario, business system, information system, grocery store, check-out system, actors, role.
St. Lukes Medical Center has a single operating room that is used by local physicians to perform surgical procedures. The cost of using the operating room is accumulated by each patient procedure and...
How do servant leaders prioritize the well-being and development of their team members, fostering a supportive environment that encourages autonomy, mastery, and purposeful engagement ?
Moab Inc. manufactures and distributes high-tech biking gadgets. It has decided to streamline some of its operations so that it will be able to be more productive and efficient. Because of this...
Let X1,..., Xn be a random sample from a n((, 2) population. Compare expected lengths of 1 - confidence intervals for that are computed assuming 2 is known. 2 is unknown.
Let X1,...,Xn be iid uniform(0, Î¸), Let Y be the largest order statistic. Prove that Y/Î¸ is a pivotal quantity and show that the interval is the shortest 1 - Î±...
Money magazine (Money, March 2003) reports percentage returns and expense ratios for top bond funds under 4 categories: US government (G), high-yield corporate (H), tax-exempt (T), and world bond...
What is the cone of depression? O the shape that the water table takes on near two pumping wells O the shape that the water table takes on near two inactive wells O the shape that the water table...
A reversible cycle may be completed in three steps, instead of the usual four. For example: (i) isothermal expansion at Th from V to V, (ii) constant-volume cooling to Tc, and (iii) adiabatic...
Coke (the beverage) is highly acidic, with a pH of 2.7! Find the concentration of hydronium ion in 900 ml of Coca-Cola. 9. Find the K, for chloride ion if for its conjugate, HC1 Ka= 1.3x106. 10. Find...
Part A The area in the center of the A band that contains no thin filaments is the OH band. I band. Ozone of overlap. O Z line. M line. Submit Request
A piece of unknown solid substance weighs 437.2 g, and requires 8460 J to increase its temperature from 19.3 C to 68.9 C. What is the specific heat of the substance? 0.0209 J/g C 0.997 J/g C 2.56 J/g...
For the following exercises, use the given information to answer the questions. The horsepower (hp) that a shaft can safely transmit varies jointly with its speed (in revolutions per minute (rpm))...
1. Use these cost, revenue, and probability estimates along with the decision tree to identify the best decision strategy for Trendy's Pies. 2. Suppose that Trendy is concerned about her probability...
WNAE, an all-news AM station, finds that the distribution of the lengths of time listeners are tuned to the station follows the normal distribution. The mean of the distribution is 15.0 minutes and...
Among U.S. cities with a population of more than 250,000, the mean one-way commute time to work is 24.3 minutes. The longest one-way travel time is in New York City, where the mean time is 38.3...
According to media research, the typical American listened to 195 hours of music in the last year. This is down from 290 hours 4 years earlier. Dick Trythall is a big country and western music fan....
10. Create the following row vector A where it has 18 elements (1 to 18). 1 4 7 10 13 16. 11 14 17 a. Use the reshape function to obtain B: == 2 5 8 3 6 9 12 15 18 b. Create a 7 element row vector...
7) Use Matlab codes to create two different vectors to separately store the numerators and denominators of the following sequence of 50 fractional numbers: 1/3, 2/5, 3/7, 4/9, 5/11, 6/13, ......,...
US exports to China have been rapidly increasing but not fast enough to offset the imports from China. This means that the United States has a/an? Give answer and explain.

Let X1,..., Xn be independent with pdfs fx, (x|) = ei-x I(i,)(x). Prove that T = mini(Xi/i)

Question:

Step by Step Answer:

The sample pdf is Thus T minX i i is sufficient by the Factorization Theorem and and ...View the full answer

Statistical Inference

Students also viewed these Statistics questions