The density f(x,y) is given by the formula f(x,y) = 8x(x + y), x ≥ 0, y ≥ 0, x + y ≤ 1 and zero otherwise.
(a) Find the marginal distributions.
(b) Find the conditional distribution of Y given X = x.
(c) Find P(X ≤ 1/2, Y ≤ 1/2)
(d) Find P(X ≤ 1/2)
(e) Find P(Y ≤ 1/2 | X ≤ 1/2)
(f) Find P(Y ≤ 1/2 | X = 1/2)
The density f(x,y) is given by the formula f(x,y) = 8x(x + y), x ≥ 0, y ≥ 0, x + y ≤ 1 and zero o...
The joint p.d.f of \(X\) and \(Y\) is given by$$ f(x, y)=\left\{\begin{array}{ll} c(1-y), & 0 \leq x \leq y \leq 1 \\ 0 & \text { otherwise. } \end{array}\right. $$Determine the value of \(c\). Find the marginal density of \(X\) and the marginal density of \(Y\) Find the conditional density of \(X\) given \(Y\). Are \(X\) and \(Y\) independent? Why? Find \(E(X-2 Y)\).
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...
Suppose X and Y are jointly distributed with density \ a. Find c. (b) Find the marginal distribution of X and Y. (c) Find P(X > 2). (d) Find (E[X2 ]). (e) Find the conditional distribution of Y, given that X = 1. (f) E[X], E[Y], E[XY], Cov(X,Y) and ρXY f(x,y)ce-(=/2+y/4) 0<y<I < 0 otherwise 0 f(x,y)ce-(=/2+y/4) 0
1. The joint probability density function (pdf) of X and Y is given by fxy(x, y) = A (1 – xey, 0<x<1,0 < y < 0 (a) Find the constant A. (b) Find the marginal pdfs of X and Y. (c) Find E(X) and E(Y). (d) Find E(XY). 2. Let X denote the number of times (1, 2, or 3 times) a certain machine malfunctions on any given day. Let Y denote the number of times (1, 2, or 3...
The joint density of X and Y is given as f(x, y) = 4xy, 0 < x, 1 and 0 < y < 1. (a). Find the marginal distribution of Y, fY (y). (b). Find E[X|Y = 1/2]. (c). Find P(X < .3|Y < .2).
The joint probability density function for continuous random variables X and Y is given below. f (x) = x + y, 0 < x < 1, 0 < y < 1 if; 0, degilse. (a) Show that this is a joint density function. (b) Find the marginal density of X . (c) Find the marginal density of Y . (d) Given Y = y find the conditional density of X . (e) P ( 1/2 < X < 1|Y =...
The joint probability density function for continuous random variables X and Y is given below. f (x) = x + y, 0 < x < 1, 0 < y < 1 if; 0, degilse. (a) Show that this is a joint density function. (b) Find the marginal density of X . (c) Find the marginal density of Y . (d) Given Y = y find the conditional density of X . (e) P ( 1/2 < X < 1|Y =...
The joint probability density function for continuous random variables X and Y is given below. f (x) = x + y, 0 < x < 1, 0 < y < 1 if; 0, degilse. (a) Show that this is a joint density function. (b) Find the marginal density of X . (c) Find the marginal density of Y . (d) Given Y = y find the conditional density of X . (e) P ( 1/2 < X < 1|Y =...
0, otherwise Let f(x,y)= 2. a. Sketch the region of integration b. Find k c. Find the marginal density of X d. Find the marginal density of Y e. Find P(Y > 0/X = 0.50) 0, otherwise Let f(x,y)= 2. a. Sketch the region of integration b. Find k c. Find the marginal density of X d. Find the marginal density of Y e. Find P(Y > 0/X = 0.50)