8. Suppose X and Y are jointly continuous with joint probability density function fx,Y(x, y) =...
Suppose that X and Y are jointly continuous random variables with joint probability density function f(x,y) = {12rºy, 1 0, 0<x<a, 0<y<1 otherwise i) Determine the constant a ii) Find P(0<x<0.5, O Y<0.25) HE) Find the marginal PDFs fex) and y) iv) Find the expected value of X and Y. Le. E(X) and E(Y) v) Are X and Y independent? Justify your answer.
Let X, Y be jointly continuous with joint density function (pdf) fx,y(x, y) *(1+xy) 05 x <1,0 <2 0 otherwise (a) Find the marginal density functions (pdf) fx and fy. (b) Are X and Y independent? Why or why not?
The joint density function of continuous variables X and Y is (8 points) fry (x, y) = x y ; 0 < x < 1, 1 < y < 5 and= 0 elsewhere. i. Find the marginal density functions for X and Y, fx (x), fy (y). ii. Are X and Y independent?. Justify your answer.
2. Let X and Y be continuous random variables with joint probability density function fx,y(x,y) 0, otherwise (a) Compute the value of k that will make f(x, y) a legitimate joint probability density function. Use f(x.y) with that value of k as the joint probability density function of X, Y in parts (b),(c).(d),(e (b) Find the probability density functions of X and Y. (c) Find the expected values of X, Y and XY (d) Compute the covariance Cov(X,Y) of X...
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...
Q.4 (22') Suppose the joint probability density function of X and Y is fx,y(x, y) = { „) - k(2 - x + y)x 0 sxs 1,0 sys1 o otherwise (a) (7”) Show that the value of constant k = 12 (b) (7') Find the marginal density function of X, i.e., fx(x). (c) (8') Find the conditional probability density of X given Y=y, i.e., fxy(xly). 11
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)....
Let X and Y be jointly continuous random variables with joint probability density given by f(x, y) = 12/5(2x − x2 − xy) for 0 < x < 1, 0 < y < 1 0 otherwise (a) Find the marginal densities for X and Y . (b) Find the conditional density for X given Y = y and the conditional density for Y given X = x. (c) Compute the probability P(1/2 < X < 1|Y =1/4). (d) Determine whether...
Let X and Y be jointly continuous random variables with joint probability density given by f(x, y) = 12/5(2x − x2 − xy) for 0 < x < 1, 0 < y < 1 0 otherwise (a) Find the marginal densities for X and Y . (b) Find the conditional density for X given Y = y and the conditional density for Y given X = x. (c) Compute the probability P(1/2 < X < 1|Y =1/4). (d) Determine whether...
[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.