a) What is the value of c?
b) Find the marginal density of Y.
c) Find E(Y).
d) Find the conditional density of X given Y, i.e., find fx|y(x|y)
e) Find E(X|Y)
f) Are X and Y independent?
a) What is the value of c? b) Find the marginal density of Y. c) Find...
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?
Q. Suppose the joint probability density function of X and Y is (a) Show that the value of constant ?=12/11 (b) Find the marginal density function of X, i.e., fX(x). (c) Find the conditional probability density of X given Y = y, i.e., fX|Y(x|y). fxy(x, y) = s k(2 - x + y)x 1 0 0 < x < 1,0 = y = 1 otherwise
Consider fx (x)=e*, 0<x and joint probability density function fx (x, y) = e) for 0<x<y. Determine the following: (a) Conditional probability distribution of Y given X =1. (b) ECY X = 1) = (c) P(Y <2 X = 1) = (d) Conditional probability distribution of X given Y = 4.
(a) Show that fY X(y; x) is a valid density function. (b) Find the marginal density of Y as a functon of the CDF (c) Find the marginal density of X. (d) Deduce P[X < 0:2]. (e) Are Y and X independent? Problem 2: Suppose (Y, X) is continuously distributed with joint density function (a) Show that fyx(y, x) is a valid density function (b) Find the marginal density of Y as a functon of the CDF Φ(t)-let φ(z)dz. (c)...
(1 point) Let x and y have joint density function p(2, y) = {(+ 2y) for 0 < x < 1,0<y<1, otherwise. Find the probability that (a) < > 1/4 probability = (b) x < +y probability =
Q1. Let X and Y have joint density 0, otherwise. a. Find the marginal densities of X and Y b. Find P(0.2 < Y < 0.31X = 0.8).
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 continuous random variables having the joint probability density 24xy, for 0 < x < 1,0<p<1.0<x+y<1 0, elsewhere Find the joint probability density of Z X + Y and W-2Y.
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.
Let X and Y be continuous random variables with joint pdf f(x,y) =fX (c(X + Y), 0 < y < x <1 otBerwise a. Find c. b. Find the joint pdf of S = Y and T = XY. c. Find the marginal pdf of T. 、