Let X and Y have a joint probability density function f(x, y) = 6(1 − y), 0 ≤ x ≤ y ≤ 1,
=0, elsewhere.
(a) Find the marginal density function for X and Y .
(b) E[X], E[Y ], and E[X − 3Y ]
Let X and Y have a joint probability density function f(x, y) = 6(1 − y),...
4. Let X and Y have joint probability density function f(x,y) = 139264 oray3 if 0 < x, y < 4 and y> 4-1, otherwise. (a) Set up but do not compute an integral to find E(XY). (b) Let fx() be the marginal probability density function of X. Set up but do not compute an integral to find fx(x) when I <r54. (c) Set up but do not compute an integral to find P(Y > X).
Let the random variables X and Y have the following joint probability density function. f (x, y) = 6(y − x), 0 < x < y < 1 If the marginal distributions are: f(x) = 3(x − 1)2, 0 < x < 1f(y) = 3y2, 0 < y < 1 Find the correlation of X and Y .
(1 point) 1. (Old Quiz Question) Let X and Y have the joint probability density function for 0 x elsewhere f(x, y)={1 f(x, y) = 1,08 ysl 0 (a) Calculate P(X - Y < 0.5) (b) Calculate P(XY <0.25) (c) Find P(X 0.75 IXY 〉 0.25)
5. Let X and Y have joint probability density function of the form Skxy if 0 < x +y < 1, x > 0 and y > 0, f(x,y)(, y) = { 0 otherwise. (a) What is the value of k? (b) Giving your reasons, state whether X and Y are dependent or independent. (c) Find the marginal probability density functions of X and Y. (d) Calculate E(X) and E(Y). (e) Calculate Cov(X,Y). (f) Find the conditional probability density function...
The joint probability density function of the random variables X, Y, and Z is (e-(x+y+z) f(x, y, z) 0 < x, 0 < y, 0 <z elsewhere (a) (3 pts) Verify that the joint density function is a valid density function. (b) (3 pts) Find the joint marginal density function of X and Y alone (by integrating over 2). (C) (4 pts) Find the marginal density functions for X and Y. (d) (3 pts) What are P(1 < X <...
3. Let the joint probability density function of W, X, Y, and Z be for,x, y, z) = elsewhere (a) Find the marginal joint probability density function fw.x(w, z). (b) Use part (a) to compute P(O< W<X<1). 3. Let the joint probability density function of W, X, Y, and Z be for,x, y, z) = elsewhere (a) Find the marginal joint probability density function fw.x(w, z). (b) Use part (a) to compute P(O
1. Let X and Y have the joint density function given by zob to todos f(x, y) = {kxy) of 50<x< 2, 0 <y<3.) i 279VHb yodmu : 1093 otherwise a) Find the value of k that makes this a probability density function. TO B 250 b) Find the marginal distribution with respect to y. 0x11 sono c) Find E[Y] d) Find V[Y]. X10 sulay boso 50
4. Let X, Y be random variables with a joint probability density function given by f(x,y) = 2, f(x,y)=0, elsewhere. 0〈x〈y〈 1; (a) Find μYlr and plot its graph. (b) Find ơ2lz and plot its graph.
Let X and Y have joint probability density function fX,Y (x, y) = e−(x+y) for 0 ≤ x and 0 ≤ y. Find: (a) Pr{X = Y }. (b) Pr{min(X, Y ) > 1/2}. (c) Pr{X ≤ Y }. (d) the marginal probability density function of Y . (e) E[XY].
3. Let the random variables X and Y have the joint probability density function 0 y 1, 0 x < y fxy(x, y)y 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)