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Applied Probability

by: Asha Walsh

Applied Probability Stat 443

Asha Walsh
GPA 3.63


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This 2 page Class Notes was uploaded by Asha Walsh on Thursday September 17, 2015. The Class Notes belongs to Stat 443 at Washington State University taught by Staff in Fall. Since its upload, it has received 50 views. For similar materials see /class/206020/stat-443-washington-state-university in Statistics at Washington State University.


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Date Created: 09/17/15
MathStat 443 Chapter 5 Review Questions 1 Let X and Y have the joint probability density function 2e7x7y O S x S lt w x y y 0 otherwise a Compute PX gt 1 l S Y S 2 Ans e 2ea ea b Find the marginal density function of X and Y fxx and fyy Ans fxltxgt2explt 2xgt fyltygt2ltexplt ygt explt 2ygtgtgt c Find the conditional density function of Y given Xx Ans eWe 2 y x 2 Two fair tetrahedra are tossed one red and one green Each has 4 faces numbered 1 2 3 4 and the face falling downward is recorded for each tetrahedron Let X represent the maximum on the two tosses and Y represent the minimum on the two tosses a Find the joint the probability function of X and Y Ans pxyl16 for xy and pxy216 for xgty xy l 2 3 M b Find the conditional probability function of X given Yl 3 The joint probability function of XY is given for a constant k by kxy O lt x lt y lt 2 fRIY 0 otherwise Find k covXY pXY Ans k5 EXl65 EY85 VX44225 VY875 EXY169 covl6225 p4 4 The random variables X Y and Z are independent with EXEYEZO and VXVYVZ2 Let U2XY Z and wxyz a Find EU and VU Find EW and VW Ans EU EWO VUl2 VW6 b Find covUW and pUW Ans covUW4 pUW47 5 The random variables X and Y have joint density function 2 7 x 2 O lt x lt l xly 3 y y otherwise a Find fyx Ans fyxx2yxl Oltxyltl 0 otherwise b Find EYXx Ans EYXx3x46xl 6 The joint p ven by Y a Compute P gt Y b Compute PX gt Y Ans lllB c Compute the marginal df of X Ans pXO29 pxlpx27lm d Compute PYllSXS2 An527 e Find EXYO and EXYl Ans 1611 and 57 respectively f Find EEXY Ans 76 g Find EX and show that it is equal to the result in f The lifetime X of a computer chip is normally distributed with mean u and standard deviation 61 Due to variations in manufacturing process p changes from batch to batch and is distributed gamma with 0c200 and 3l ie HGam0c2003l Compute EX and VX Hint Use conditional expectations Ans EX20 VX3


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