Mathematical Statistics STAT 710
Popular in Course
Popular in Statistics
Mrs. Triston Collier
verified elite notetaker
This 2 page Class Notes was uploaded by Mrs. Triston Collier on Thursday September 17, 2015. The Class Notes belongs to STAT 710 at University of Wisconsin - Madison taught by Staff in Fall. Since its upload, it has received 16 views. For similar materials see /class/205090/stat-710-university-of-wisconsin-madison in Statistics at University of Wisconsin - Madison.
Reviews for Mathematical Statistics
Report this Material
What is Karma?
Karma is the currency of StudySoup.
You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!
Date Created: 09/17/15
TA Yuan Jiang Email jiangy statwiscedu STAT 710 Discussion 25 April 297 2008 1 Lengths of Con dence Intervals Example 1 Let X X1L7 Xn n gt 1 be a random sample from the exponential distribution on the interval 67 00 with scale parameter 67 where 6 gt 0 is unknown i Show that both X6 and X16 are pivotal quantities7 where X is the sample mean and X1 is the smallest order statistic ii Obtain con dence intervals with con dence coef cient 1 704 for 6 based on the two pivotal quantities in iii Discuss which con dence interval in ii is better in terms of the length Example 2 Let 6 gt 0 be an unknown parameter and T gt 0 be a statistic Suppose that T6 is a pivotal quantity having Lebesgue density f and that x2f is unimodal at 0 in the sense that f is nondecreasing for x 3 0 and fx is nonincreasing for z 2 x0 Consider the following class of con dence intervals for 6 b Cb 1T7a 1Tagt0bgt0fzdz17a Show that if bg1T7ang E C7afa1 bf br gt 07 and a1 3 x0 3 in7 then the interval bg1T7ang has the shortest length within C Example 3 Let X1Xn be a random sample from NM7027 u E R and 02 gt 0 i Suppose that u is known Let an and bn be constants satisfying aflfnmn bifnbn gt 0 and fndz 1 7 a where fn is the Lebesgue den sity of the chi square distribution xi Show that the interval bg1T7ang has the shortest length within the class of intervals of the form b lT7 a lT7 f fndz 17 a where T 21Xi 7 2 ii When u is unknown7 show that 6101 7 1Szal1n 7 1SZ has the shorest length within the class of 1 7 a con dence intervals of the form b 1n 7 1Sza 1n 7 1SZ7 where 52 is the sample variance iii Find the shortest length interval for 039 within the class of con dence Of ce 1275A M80 1 Phone 262 1577 TA Yuan Jiang Email jiangy statwiscedu intervals of the form b lZxn 7157a 12xn 717 where 0 lt a lt b lt 007 and fn1zdx 17 a Of ce 1275A M80 2 Phone 262 1577
Are you sure you want to buy this material for
You're already Subscribed!
Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'