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Let (X,Y) have joint pdf given by f(x, y) = { Sey, 0 < x <y<, | 0, 0.W., (a) Find the correlation coefficient px,y (b) Are X and Y independent? Explain why.
Let (X,Y) have joint pdf given by sey, 0 < x < y < 0, f(x, y) = { ( 0, 0.W., (a) Find the correlation coefficient px,y: (20 pts) (b) Are X and Y independent? Explain why. (10 pts)
4. Suppose X and Y have the joint pdf f(x,y) = 6x, 0 < x < y < 1, and zero otherwise. (a) Find fx(x). (b) Find fy(y). (c) Find Corr(X,Y). (d) Find fy x(y|x). (e) Find E(Y|X). (f) Find Var(Y). (g) Find Var(E(Y|X)). (h) Find E (Var(Y|X)]. (i) Find the pdf of Y - X.
4. (30 pts) Let (X,Y) have joint pdf given by e-y, 0 < x < y < 0, f(x,y) = { | 0, 0.w., (a) Find the correlation coefficient px,y. (20 pts) (b) Are X and Y independent? Explain why. (10 pts)
4. (30 pts) Let (X,Y) have joint pdf given by < , | e-9, 0 < x < f(x,y) = 3 | 0, 0.w., (a) Find the correlation coefficient px,y: (20 pts) (b) Are X and Y independent? Explain why. (10 pts)
7. Suppose X and Y have joint pdf f(x,y) = 24x y if x >0, y>0,x+y<1 and 0 otherwise. Find P(Y > 2x).
Suppose X, Y are random variables whose joint PDF is given by . 1 0 < y < 1,0 < x < y y otherwise 0, 1. Find the covariance of X and Y. 2. Compute Var(X) and Var(Y). 3. Calculate p(X,Y).
5.5.5 X and Y are random variables w the joint PDF X,Y (z, y) = 0 otherwise. (a) What is the marginal PDF fx()? (b) What is the marginal PDF fr(v)?
Suppose X and Y are jointly continuous random variables with joint density function Let U = 2X − Y and V = 2X + Y (i). What is the joint density function of U and V ? (ii). Calculate Var(U |V ). 1. Suppose X and Y are jointly continuous random variables with join density function Lei otherwise Let U = 2X-Y and V = 2X + y (i). What is the joint density function of U and V? (ii)....
Suppose X, Y are random variables whose joint PDF is given by fxy(x,y) = { 0<y<1,0<=<y 0, otherwise 1. Find the covariance of X and Y. 2. Compute Var(X) and Var(Y). 3. Calculate p(X,Y)