2.8.14 Let X and Y have joint density fX,Y (x, y) = (x2 + y)/36 for −2 < x < 1 and 0 < y < 4, otherwise fX,Y (x, y) = 0.
(a) Compute the conditional density fY|X (y|x) for all x, y ∈ R1 with fX (x) > 0.
(b) Compute the conditional density fX|Y (x|y) for all x, y ∈ R1 with fY (y) > 0.
(c) Are X and Y independent? Why or why not?
2.8.14 Let X and Y have joint density fX,Y (x, y) = (x2 + y)/36 for...
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?
. (Dobrow, 1.13) Random variables X and Y have joint density fX,Y = ( 3y 0 < x < y < 1 0 otherwise (a) Find the conditional density of Y given X = x. (b) Compute E[Y | X = x]. (c) Find the conditional density of X given Y = y. Describe the conditional distribution. I. (Dobrow, 1.13) Random variables X and Y have joint density 0 otherwise (a) Find the conditional density of Y given X (b)...
1. Let (X,Y) be a random vector with joint pdf fx,y(x,y) = 11–1/2,1/2)2 (x,y). Compute fx(x) and fy(y). Are X, Y independent? 2. Let B {(x,y) : x2 + y2 < 1} denote the unit disk centered at the origin in R2. Let (X',Y') be a random vector with joint pdf fx',y(x', y') = 1-'13(x',y'). Compute fx(x') and fy(y'). Are X', Y' independent?
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...
2.6.9 Let X have density function fx(x) = x/4 for 0 < x < 2, otherwise fx(x)=0. (a) Let Y = X. Compute the density function fy(y) for Y. (b) Let Z = X. Compute the density function fz(z) for Z.
The joint probability density function of random variables X and Y is given by f(x,y) ={10xy^2 0≤x≤y≤1,0 otherwise. (a) Compute the conditional probability fX|Y(x|y). (b) Compute E(Y) and P(Y >1/2). (c) Let W=X/Y. Compute the density function of W. (d) Are X and Y independent? Justify briefly.
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...
1. Let X and Y be continuous random variables with joint pr ability density function 6e2re5y İfy < 0 and x < otherwise. y, fx,y (z,y) 0 (a) [3 points] Show that the marginal density function of Y is given by 3es if y 0, 0 otherwise. fy (y) = (b) |3 poin s apute the marginal density function of X (c) [3 points] Show that E(X)Y = y) =-y-1, for y 0 (d) 13 points] Compute E(X) using the...
The joint probability density function of random variables X and Y is given by f(x,y) ={10xy^2 0≤x≤y≤1,0 otherwise. (a) Compute the conditional probability fX|Y(x|y). (b) Compute E(Y) and P(Y >1/2). (c) Let W=X/Y. Compute the density function of W. (d) Are X and Y independent? Justify briefly.