The random variables X and Y have the joint density: fxy(x,y) = 2-x-y, for 0
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- Given the random variables X and Y having the following joint density: f(x, y) = 2(x + y) for 0 < y < x < 1. A) Compute the conditional pdfs: fX│Y (x) and fY│X (y). B) Are X and Y independent?Let X and Y be two independent random variables with densities fX(x) = e^(-x), for x>0 and fY(y) = e^y, for y<0, respectively. Determine the density of X+Y.Suppose that the random variables X and Y have a joint density function f(x,y).prove that Cov(X,Y)=0 if E(X|Y=y) does not depend on y
- The random variables X and Y have the following joint probability density function:f(x,y)={e−x−y , 0<x<∞; 0, elsewhere. What is Cov(X,Y)(X,Y)?If the joint density of X and Y is given byf(x, y) =⎧⎨⎩e−(x+y) for x > 0, y > 00 elsewhere and Z = X + Y2 , find the probability density of Z by thedistribution function technique.For random variables X and Y with joint density function f(x,y) = 6e^-2x-3y. (x,y > 0) and f(x,y) = 0 otherwise, find: Are X and Y independent? Give a reason for your answer.
- Suppose that the random variables X and Y have a joint density function given by: f(x,y)={cxy for 0≤x≤2 and 0≤y≤x, 0 otherwise Find the constant c, P(Y≥1/2), P(X < 2, Y >1/2), P(X < 1), Determine whether X and Y are independent.If X has the uniform density with the parameters α = 0and β = 1, use the distribution function technique to findthe probability density of the random variable Y = √X.Find the moment generating function for the random variable X whose density function is f(x). fx = 2x 0<x<1 MX(t) = _______________________________________
- Suppose that the random variables X and Y have a joint density function given by: f(x,y)={cxy for 0≤x≤2 and 0≤y≤x, 0 otherwise c=1/2 P(X < 1), Determine whether X and Y are independentThe PDF of a continuous random variable X is as follows: f(X)= c(4x2 - 2x2) 0<* x <* 2 (*less or equal to) a. For this to be a proper density function, what must be the value of c ?Use the rejection method to generate a random variable having density function f(x) = kx1⁄2e−x , x > 0 where k =1/Γ (3/2) =2√π