
How to get the cdf when y>x>0? Thanks

How to get the cdf when y>x>0? Thanks 6. The joint probability density function (pdf) of...
The joint probability density function (pdf) of (X,Y ) is given by f(X,Y )(x,y) = 12/ 7 x(x + y), for 0 ≤ y ≤ 1, 0 ≤ x ≤ 1, 0, elsewhere. (a) Find the cumulative distribution function of (X,Y ). Make sure you derive expressions for the cdf in the regions • x < 0 or y < 0; • 0 ≤ x ≤ 1, 0 ≤ y ≤ 1; • x > 1, 0 ≤ y ≤...
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 probability density function (PDF) of random variables X and Y is given by: f(x,y) = 4xy for 0 ≤ y ≤ x ≤ 1, and = 0 elsewhere The mean of the random variable X is:
the joint probability density function of X and Y is given by f(x,y)={e-(x+y) for X>0, y>0 and 0 elsewhere A. Find the marginal density of X B. Find the marginal density of Y C. Find the Conditional density of X given Y D. Are random variables X and Y independent? State the reason of your answer. E. Find P(X<.5, y<.5) F. Find P(X=.5, y<.5)
3. Let the random variables X and Y have the joint probability density function fxr (x, y) = 0 <y<1, 0<xsy 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).
1. Consider the joint probability density function 0<x<y, 0<y<1, fx.x(x, y) = 0, otherwise. (a) Find the marginal probability density function of Y and identify its distribution. (5 marks (b) Find the conditional probability density function of X given Y=y and hence find the mean and variance of X conditional on Y=y. [7 marks] (c) Use iterated expectation to find the expected value of X [5 marks (d) Use E(XY) and var(XY) from (b) above to find the variance of...
< 1. The joint probability density function (pdf) of X and Y is given by for(x, y) = 4 (1 - x)e”, 0 < x <1, 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).
the joint probability density
function is given by
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).
Consider a continuous random vector (Y, X) with joint probability density function F(x,y) = e-y for 0<x<y<∞ Compute the marginal density of X denoted by f(x). Compute the conditional density of Y given X denoted by f(y|x). Hint: Consider the two cases y > x and y ≤ x separately. Compute the conditional expectation E[Y |X = x]. Compute the conditional variance Var(Y |X = x).
9. Let the joint density function of (X, Y) be E (0, oo fa,y) ye e forx (O,co) and y (o, co) (a) [4 points] Find fr) and fxy(xly) (b) [3 points] Compute the conditional expectation E(XIY). (c) [3 points] Find P(X > 3Y 1)