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 36 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 10 October 167 2007 1 Uniformly Integrable Example 1 Let Xn be a sequence of random variables de ned on 971213 Show that Xn is uniformly integrable if and only if it satis es the following two conditions i For any 8 gt 07 there exist a 6 gt 0 such that for any A E f with P A S 6 we have supn E anllA S 6 ii suan lt oo 2 Law of Large Numbers Example 2 Let YZ7 Z1 239 17 27 771 be iid random 2 Vectors Assume that EYE lt 007EZ12 lt 00 The sample correlation coe cient is de ned as 222106 YZi 7 Z T n71SySZ 7 where 7 2 Y SY Zi1Yz Y 7171 Nl l n 7 2 22 SZ Zi1zl Z 7171 C Z17 Le p 1Vari11Varzl39 Show that T all Y p7 where p is the correlation coef cient between Y1 and ova121 3 Quiz 4 855 am 910 am Of ce 1275A M80 1 Phone 262 1577
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