INTRO STAT THEORY I
INTRO STAT THEORY I STAT 702
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This 4 page Class Notes was uploaded by Shane Marks on Monday October 26, 2015. The Class Notes belongs to STAT 702 at University of South Carolina - Columbia taught by Staff in Fall. Since its upload, it has received 8 views. For similar materials see /class/229677/stat-702-university-of-south-carolina-columbia in Statistics at University of South Carolina - Columbia.
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Date Created: 10/26/15
STAT 702J702 November 9th 2006 Lecz ure 27 lnstruotor Brian Habing Department of Statistics Telephone 8037773578 Email habingstatsoedu M STAT 702702 BHabing Univ of SC 3 Exam 2 1 Let X and Y be independent random variables where X is exponential with k3 and Y is normal with p2 and 629 Find EXY and VarXY STAT 702702 BHabing Univ of SC 3 2 Find k such that fX kX2 X on OltXlt2 and is O elsewhere is a pdf M STAT 702702 BHabing Univ of SC 3 3 Let the random variable X have cdf FX 121 X3 on 1SXS1 and 0 otherwise Find EX and VarX V STAT 702702 BHabing Univ of SC 3 4 Leaks due to manufacturing defects occur in a brand of hose at a rate of approximately 2 per 500 feet Name an appropriate distribution and estimate the probability that the first defect will be found in the first 100 feet STAT 702702 BHabing Univ ofSC 5 Evaluate 0 4 x e 7rde 0 STAT 702702 BHabing Univ ofSC 6 Let X have a exponential with k1 Find the Cdf and pdf for Y1e39X STAT 702702 BHabin Univ of SC g M13an 7 Let I YXy on 1ltXlt11ltylt1 and be 0 othenNise Find the conditional distributions of XY and YX Also are X and Y independent STAT 702702 BHab1n Un1V of SC M g rrrii fl lun 8 Let X and Y be independent Chi square random variables with 1 degree of freedom The pdf is on page 61 Derive the pdf of ZXN STAT 702702 BHab1n Un1V of SC M g rrrii fl lun 9 In Class we showed how to get general formula s for the pdf s of ZXY and ZXY Show that if X and Y have joint pdf I YXy and ZXY that f2 2 fl fnlx jidx x lxl STAT 702702 BHabin Univ of SC g M13an 10 10 Let X and Y have joint pdf mm 1 lt12xgtlt12ygt on OltXlt1Oltylt1 and be 0 elsewhere Find the joint pdf of UXY and VX2Y STAT 702702 BHabing Univ of SC r M 11 11 Let X1X5 be independent exponential random variables with parameter 9L1 Find the pdf for the median X3 STAT 702702 BHabing Univ ofSC r M 12