1.

Given,Then find,

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Answer:

LET X1, X2, and X3 be three i.i.d Bernoulli(p) random variables andY1=max(X1,X2),Y2=max(X1,X3),Y3=max(X2,X3),Y=Y1+Y2+Y3.Find EY and Var(Y).Let X,YX,Y and ZZ be three jointly continuous random variables with JOINT PDF

fXYZ(x,y,z)=⎧⎩⎨⎪⎪13(x+2y+3z)00≤x,y,z≤1otherwisefXYZ(x,y,z)={13(x+2y+3z)0≤x,y,z≤10otherwise

Find the joint PDF of XX and YY, fXY(x,y)fXY(x,y).



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