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plz solve |
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Answer» Let X,Y and Z be three jointly continuous random variables with joint PDF fXYZ(x,y,z)=⎧⎩⎨⎪⎪13(x+2y+3z)00≤x,y,z≤1otherwise Find the joint PDF of X and Y, fXY(x,y).Let X,Y and Z be three independent random variables with X∼N(μ,σ2), and Y,Z∼Uniform(0,2). We also know that E[X2Y+XYZ]=13,E[XY2+ZX2]=14. Find μ and σ.Let X1, X2, and X3 be three i.i.d BERNOULLI(p) random variables and Y1=max(X1,X2),Y2=max(X1,X3),Y3=max(X2,X3),Y=Y1+Y2+Y3. Find EY and VAR(Y).Let MX(s) be finite for s∈[−c,c], where c>0. Show that MGF of Y=aX+b is given by MY(s)=esbMX(as), and it is finite in [−c|a|,c|a|]Let Z∼N(0,1) Find the MGF of Z. Extend your result to X∼N(μ,σ) |
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