Let X1, ,Xn be iid uniform(0, Icirc cedil ), Let Y be the largest order statistic Prove that Y Icirc cedil is a pivotal quantity and show that the interval is the shortest 1 Icirc plusmn pivotal interval 0 y5e n al n...

a The density of Y X n is f Y y ny n1 n 0 y So is a scale parameter and T Y is a pivotal qua ...

Let X1,...,Xn be iid uniform(0, Î¸), Let Y be the largest order statistic. Prove that Y/Î¸ is

Question:

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± pivotal interval.

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 Y be the largest order statistic of a random sample of size n from a distribution with pdf f(x | ) = 1/, 0 where > 0, > 0. (a) If w(Y) is the Bayes estimator of and [ w(Y)]2 is the loss...
Prove Theorem 6.2.10. Let X1,..., Xn be iid observations from a pdf or pmf f(x|Î¸) that belongs to an exponential family given by where Î¸ = (Î¸1, Î¸2,...
Let X1,..., Xn be iid n(Î¸, Î¸2), Î¸ > 0. For this model both and cS are unbiased estimators of Î¸, where (a) Prove that for any number a the estimator...
What is the relationship between group norms and group cohesiveness? What roles do both cohesiveness and norms plan in shaping group performance?
What is the difference between authorized shares and outstanding shares?
The results of two CD triaxial tests at different confining pressures on medium dense, cohesionless sand are summarized in the table below. The void ratios of both specimens were approximately the...
Explain the difference between a. Actors and stakeholders. b. Primary and supporting actors.
Jerry Trickett, a retired army officer, opened Tricketts Catering Service. As his accountant, analyze the transactions listed and present them in proper form. a. The analysis of the transactions by...
Calculate Rm (market return from market price index) and Rj (return of share prices). Date PERIOD 1 AORD R company m m Feb-14 5403 0.008 0.3370 Mar-14 5470.8 0.008 0.3354 Apr-14 5473.8 0.008 0.3298...
A basic wooden railway set contains the pieces shown in Figure 3.32. The task is to connect these pieces into a railway that has no overlapping tracks and no loose ends where a train could run off...
Let X1,..., Xn be independent with pdfs fx, (x|) = ei-x I(i,)(x). Prove that T = mini(Xi/i) is a sufficient statistic for 6. Based on T, find the 1 - confidence interval for of the form [T + a, T +...
Prove a special case of Theorem 9.3.2. Let X ~ f{x), where / is a symmetric unimodal pdf. For a fixed value of 1 - , of all intervals [a, b] that satisfy ba f(x)dx= 1 - , the shortest is obtained by...
For the given points A, B, and C, find the area of the triangle with vertices A, B, and C. A(-1, -5, -3), B(-3, -2, -1), C(0, -5, -1)
Agriculture accounted for 3/8 of greenhouse gas emissions in 1980 and 2/11 in 2000. What's the relative change in greenhouse emissions from agriculture between 1980 and 2000? 20.1% 19.3% 51.5% 48.3%...
NH3 is a weak base (Kb = in NH4Cl at 25 C? pH = 5.539 1.8 x 10-5) and so the salt NH4Cl acts as a weak acid. What is the pH of a solution that is 0.047 M
(2) - Agt! Predict products and write balanced FUE and NIE equations for the following precipitation reactions. i) silver(I) nitrate with sodium nitrate Ag No3 + Na No3 - Ag No3 + NaNO3 No3 Not, Nos...
Glycolysis starts with and ends with two glucose; one pyruvate molecule one glucose; one pyruvate molecule one glucose; two pyruvate molecules one glucose; four ATP molecules
How many electrons at a time are passed between the pigmen molecules in the light-harvesting complexes? O 0 0 1 O 2 O 3 O 4
For the following exercises, list all possible rational zeros for the functions. f(x) = 6x 4 10x 2 + 13x + 1
A summary of changes in Pen Corporation's Investment in Sam account from January 1, 2011, to December 31, 2013, follows (in thousands): ADDITIONAL INFORMATION 1. Pen acquired its 80 percent interest...
Assume a binomial probability distribution with n 5 50 and p 5 .25. Compute the following: a. The mean and standard deviation of the random variable. b. The probability that x is 15 or more. c. The...
Assume a binomial probability distribution with n 5 40 and p 5 .55. Compute the following: a. The mean and standard deviation of the random variable. b. The probability that x is 25 or greater. c....
Dotties Tax Service specializes in federal tax returns for professional clients, such as physicians, dentists, accountants, and lawyers. A recent audit by the IRS of the returns she prepared...
5) Write Matlab expressions to extract only the elements at odd positions in a vector (i.e. the 1st, 3rd, 5th, 7th..., elements of the vector), regardless of the length of the vector. Make sure your...
1. Convert NFA to DFA 91 1 0 a. b. (92) 1 (93) 1. 90 1 0,1 0,1 (92)
1. (15 pts) Given matrix X, where each row represents a different data point. You are asked to perform k-means clustering on this dataset using the Euclidean distance as the distance function. Here k...

Let X1,...,Xn be iid uniform(0, Î¸), Let Y be the largest order statistic. Prove that Y/Î¸ is

Question:

0: y5e n} al/n

Step by Step Answer:

a The density of Y X n is f Y y ny n1 n 0 y So is a scale parameter and T Y is a pivotal qua...View the full answer

Statistical Inference

Students also viewed these Statistics questions