[Steps Shown] The joint p.d.f. of the random variables X and Y is given by f_X,Y(x,y)= A(1-x) 0≤ x≤ 1,0≤ y≤ 1 , 0 otherwise , Find A. (b) Let
Question: The joint p.d.f. of the random variables X and Y is given by
\({{f}_{X,Y}}\left( x,y \right)=\left\{ \begin{aligned} & A\left( 1-x \right)\,\,\,0\le x\le 1,0\le y\le 1 \\ & 0\text{ otherwise} \\ \end{aligned} \right.\)- Find A. (b) Let Z = XY . Find \({{f}_{Z}}\left( z \right)\)
Deliverable: Word Document 
(Step-by-Step) Suppose the density function of X is an even function.
![[See Solution] Suppose X and Y are](/images/solutions/MC-solution-library-72196.jpg "[See Solution] Suppose X and Y are independent normal random variables.")
[See Solution] Suppose X and Y are independent normal random variables.
![[Step-by-Step] X and Y are i.i.d. with](/images/solutions/MC-solution-library-72197.jpg "[Step-by-Step] X and Y are i.i.d. with exponential densities f_X(x)=e^-xu(x)")
[Step-by-Step] X and Y are i.i.d. with exponential densities f_X(x)=e^-xu(x)
(Steps Shown) Prove that for any X , Y real or complex, | E(XY) |^2≤
![[Solution] X and Y are i.i.d. random](/images/solutions/MC-solution-library-72199.jpg "[Solution] X and Y are i.i.d. random variables uniform in (0, 1).")
[Solution] X and Y are i.i.d. random variables uniform in (0, 1).
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