Question

$( \frac{1}{2} y {}^{2} - \frac{1}{3} y - 1) - ( \frac{1}{3} y {}^{2} - \frac{1}{2} y - 3) - ( \frac{1}{4} y {}^{2} - \frac{1}{3} y - \frac{1}{2} )$

plz solve ​

Answer 1

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)