Mathematical Statistics STAT 709
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Mrs. Triston Collier
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This 1 page Class Notes was uploaded by Mrs. Triston Collier on Thursday September 17, 2015. The Class Notes belongs to STAT 709 at University of Wisconsin - Madison taught by Staff in Fall. Since its upload, it has received 38 views. For similar materials see /class/205087/stat-709-university-of-wisconsin-madison in Statistics at University of Wisconsin - Madison.
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Date Created: 09/17/15
TA Yuan Jiang Email jiangy statwiscedu STAT 709 Discussion 12 October 237 2007 1 LocationScale Families Example 1 Let X1L7 7X be a random sample from the exponential distribution with Lebesgue density 6 16 1 mlQIQXz7 where a E R and 6 gt 0 are parameters Let X1 S S XW be order statistics7 X0 07 and Z X 7 X011 239 17 quot771 Show that a Z1 Zn are independent and 2 717271 Z 6 has the 2 distribution 7 7 X2 7 b 2Z1 X n 7 rXT 7 71646 has the x distribution7 r 17 quot771 c X1 and Y are independent and X17aY has the Lebesgue density n1 fn om t where M Y n 1111XltigtXlt1gt Note Z Exp06 xi 2 Minimal Suf ciency Example 2 a Let X17 7X i39iw39d39 NW M2 M E R Find a minimal suf cient statistic for M b Let X1 Xn U661 9 e R Show that TX X1Xn is minimal suf cient for 6 Example 3 Let X17Y17 7 XmYn are iid samples from the bivariate normal distribution X 0 1 6 YNlolvle l with 6 E 9 7171 Find a minimal suf cient statistic Of ce 1275A M80 1 Phone 262 1577
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