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Math-353-25.pdf - First Mid Term, S2-1442H M 380 –...

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1ــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــAnswer the following questions:Q1: [5+3]a)Let120if0... +if0NNbea random sum and assume thatE()=, E()=kNand22Var()=, Var()=kNProve thatE(X)=and222Var(X)= b)Let us model the daily stock price change as1...NZ, where01,,...,Nare independent normally distributed random variables with commonmean zero and variance 0.5, andNis the number of transactions during the daywhich has a Poisson distribution with mean 1.(i) Determine the mean and variance ofZ(ii) What is the distribution ofZQ2: [5+4]a) Given the following joint distribution.000.10.410.30.2Compute(X,Y)XYX=N0.?1.King Saud UniversityCollege of SciencesDepartment of MathematicsFirst Mid Term, S2-1442HM 380Stochastic ProcessesTime: 90 minutes
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Term
Fall
Professor
NoProfessor
Tags
Normal Distribution, Variance, Probability theory, probability density function, x n, E

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