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Consider random variables X N ( 1 , 2 ) and Y N ( 0 , 4 ) , let also c = c o

Consider random variablesXN(1,2) and YN(0,4), let alsoc=cov(X,Y)

a) Denote Z=(X,Y). Find E(Z) andVar(Z)

b) Find the correlation coefficient (2X1,5Y) for c=0.5

c) Consider the case when c=0. Are X and Y independent from each other? Why or Why not?

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