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by: Shane Marks


Shane Marks

GPA 3.93


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Class Notes
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This 6 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 27 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 September 16th 2004 Lecfure 9 lnstructor Brian Habing Department of Statistics Telephone 8037773578 Email habingstatscedu V4 STAT 702J702 BHabing Univ ofSC Today Homework Solutions Poisson Distribution Continuous Random Variables STAT 702J702 BHabing Univ ofSC w Ch 4 45 EXEYy but oxicy Let ZocX1ocY a Show that EZu b Find or in terms of ox and oy to minimize VarZ STAT 702J702 BHabing Univ ofSC w 0 Under what circumstances is it better to use the average XY2 than either X or Y alone STAT 702J702 BHabing Univ ofSC w 215 Poisson Process A Poisson process with parameter 7 is a model for events that occur over time or space etc such that STAT 702J702 BHabing Univ ofSC w 1 Occurrences of events in non overlapping intervals are independent 2 The probability of exactly one change in an interval of length his M7 o7 3 The probability of two or more occurences in an interval of length his o7 STAT 702J702 BHabing Univ ofSC w Examples include o The number of radioactive particles emitted by a radioactive isotope Number of people arriving in a line The number of phone calls arriving at a telephone exchange w STAT 702J702 BHabing Univ ofSC A Poisson process is very similar to a binomial experiment where the small subintervals constitute the trials and X is the number of occurrences In fact we can derive the pdf of the Poisson distribution by taking a binomial and letting n m and np 67 xxx STAT 702J702 BHabing Univ ofSC For the Poisson Distribution we have X PX x iL e7L x X A 2 OXZll xxxx STAT 702J702 BHabing Univ ofSC Example Between 2am and 4am cars pass the mile marker at a rate of 24 per hour What is the probability that 0 cars will pass in a 5 minute span One car What is the expected number of cars to pass by in the minute span STAT702J702 BHabing Univ ofSC 10 How long until the next car passes V STAT702J702 BHabing UnivofSC 11 22 Continuous Variables Consider a random number generator that selects a real number at random from between 0 and 1 V STAT702J702 BHabing UnivofSC 12 The probability density function pdf fX satisfies the following a fx 2 0 for all X b lofxdx 1 C PaltXltbllfxdx w STAT 702J702 BHabing Univ ofSC 4 w 13 The cdf is defined the same way FX Psz ifxdx STAT 702J702 BHabing Univ ofSC w M For expected values we need to change the summation into an integral EXzxpx 2 loxfxdx Varoo 2x y2px 2 x ymxwx STAT 702J702 BHabing Univ ofSC V4 Three notes fxF x Pa ltXltbFb Fa 39 PXltXlt Xdxz fXdX w STAT 7021702 BHabing Univ ofSC M 16


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