2. Suppose X and Y are continuous random variables with joint density function f(x, y) =...
4. Let X and Y be continuous random variables with joint density function f(x, y) = { 4x for 0 <x<ys1 otherwise (a) Find the marginal density functions of X and Y, g(x) and h(y), respectively. (b) What are E[X], E[Y], and E[XY]? Find the value of Cov[X, Y]
8), Let X and Y be continuous random variables with joint density function f(x,y)-4xy for 0 < x < y < 1 Otherwise What is the joint density of U and V 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.
Suppose X and Y are continuous random variables with joint density function 1 + xy 9 fx,y(2, y) = 4 [2] < 1, [y] < 1 otherwise 0, (1) (4 pts) Find the marginal density function for X and Y separately. (2) (2 pts) Are X and Y independent? Verify your answer. (3) (9 pts) Are X2 and Y2 independent? Verify 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...
Suppose that X and Y are jointly continuous random
variables with joint density
f(x, y) = (
ye−xy 0 < x < ∞, 1 < y < 2
0 otherwise
(a) Given that X > 1, what is the expected value of Y ? That is,
calculate E[Y | X > 1].
(b) Given that X > Y , what is the expected value of X? For this
part, you are only required
to set up the requisite integrals, but...
Let X and Y be joint continuous random variables with
joint density function
f(x, y) = (e−y
y
0 < x < y, 0 < y, ∞
0 otherwise
Compute E[X2
| Y = y].
5. Let X and Y be joint continuous random variables with joint density function e, y 0 otwise Compute E(X2 | Y = y]
24. Let X and Y be continuous random variables with joint density function 4xy for 0 < x, y 1 f(x, y) otherwise. What is the probability of the event X given that Y ?
[1] The joint probability density function of two continuous random variables X and Y is fxy(x, y) = {0. sc, 0 <y s 2.y < x < 4-y = otherwise Find the value of c and the correlation of X and Y.
)on 4. Suppose X and y are continuous random variables with joint density funstion the unit square [0, 1] x [0, 1]. (a) Let F(r,y) be the joint CDF. Compute F(1/2, 1/2). Compute F(z,y). (b) Compute the marginal densities for X and Y (c) Are X and Y independent? (d) Compute E(X), E(Y), Cov(X,y)