The topic is multivariate random variables. We have to solve the given questions.
1 Let X and Y be jointly Continuous random variables with joint PDF given by:
fXY(x,y)=4xy I(0,1) I(0,1)(y)
Obtain the following:
a. Joint CDF ofXand Y
b. Marginal CDF of X using (a)
c. Marginal CDF of Y using (a)
d. Marginal PDF ofXusingfx(x,y)
e. Marginal PDF of Y usingfr (x,y)
f. Conditional PDF of Y given X
g. E(XY)
h. E(X) and E(X2) using (d)
i. E(Y) and E(Y2) using (e)
j. Var(X) and Var(Y) using (h) and (i)
k. Cov(X,Y) using (g), (h) and (j)
I. Corr(X,Y)
2. Given below is the joint CDF of X and Y.
Obtain the following:
a. Joint PMF of X and Y (present it in tabular form)
b. Marginal PMF of X
e. Marginal PMF of Y
d. Marginal CDF of X using (b)
e. Marginal CDF of Y using (e)
f. E(XY) using (a)
g. E(X) and E(X2) using (b)
h. E(Y) and E(Y2) using (e)
i. Var(X) and Var(Y) using (g) and (h)
j. Cov(X.Y) using (f). (g) and (h)
k. Corr(X,Y)
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