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Math-353-20.pdf - First Mid Term, S1-1441H M 380 -...

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1ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــAnswer the following questions:Q1: [4+4]a) Ifexp( )Tprove that:()(),0pr Tts Tspr Ttb) The lifetimeTof a certain component has an exponential distribution withparameterλ=0.02. Find pr(120100)TQ2: [4+5]a) The joint probability density function of the two random variablesXandisf(x,y)=8xy ,0xy1. Find3Y Xf(y)b) Given the joint probability mass functions of two random variablesXandas in the following table:1201/80101/4201/431/80i) Find(X,Y)ii) Determine whetherXandYare two independent random variables or not?Justify your answer.XYtsTY1Y301/81/80King Saud UniversityCollege of SciencesDepartment of MathematicsFirst Mid Term, S1-1441HM 380 - Stochastic ProcessesTime: 90 minutes

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Term
Fall
Professor
NoProfessor
Tags
Probability theory, probability density function, King Saud University, Department of Mathematics, T exp

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