aercise 6.43. Let the random variables X, Y have joint density function 2r y + vy, ifo<r< 1 and 0< fx,y(x, y)...
sity functions. Exercise 6.46. Let X, Y be independent random variables with density functions fx and fy. Let T- min(X, Y) and V max(X, Y). Use the joint density function fr v from equation (6.31) to compute the marginal density functions fr of T and fv of 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)....
3. Let the random variables X and Y have the joint probability density function 0 y 1, 0 x < y fxy(x, y)y otherwise (a) Compute the joint expectation E(XY) (b) Compute the marginal expectations E(X) and E (Y) (c) Compute the covariance Cov(X, Y)
4. The random variables X and Y have joint probability density function fx,y(x, ) given by: fx,y(x, y) 0, else (a) Find c. (b) Find fx(x) and fy (), the marginal probability density functions of X and Y, respectively (c) Find fxjy (xly), the conditional probability density function of X given Y. For your limits (which you should not forget!), put y between constant bounds and then give the limits for in terms of y. (d) Are X and Y...
55. Let X and Y be jointly continuous random variables with joint density function fx.y(x,y) be-3y -a < x < 2a, 0) < y < 00, otherwise. Assume that E[XY] = 1/6. (a) Find a and b such that fx,y is a valid joint pdf. You may want to use the fact that du = 1. u 6. и е (b) Find the conditional pdf of X given Y = y where 0 <y < . (c) Find Cov(X,Y). (d)...
. Let X and Y be two random variables with joint probability density function fx,y(x, y)-cy for 0 x 1 and 0 y 1. (Note: fxy(x,y) = 0 outside this domain ) (a) Find the marginal distribution fx(x). (b) Find the value of constant c, using the fact that fx,y(x, y) dx dy = 1.
1. Suppose X and Y are jointly continuous random variables with joint density function otherwise Let U 2X-Y and V-2X +Y (i). What is the joint density function of U and V? (ii). Caleulate Var(UV)
1. Suppose X and Y are jointly continuous random variables with joint density function otherwise Let u=2x-Yand, V = 2X + Y (i). What is the joint density function of U and V? (ii). Calculate Var(UIV).
Random variables X and Y have the following joint probability density function, fx,y(x, y) = {c)[4] < 15.36, 1y| < 15.367 1.36} 0, 0.w. where cis a constant. Calculate P(Y – X| < 8.41).
[1] The joint probability density function of two continuous random variables X and Y is fx,x(x, y) = {6. sc, 0 <y s 2.y = x < 4-y otherwise Find the value of c and the correlation of X and Y.