7. Let X and Y have joint probability mass function fx,y(x,y) = (z+y)/30 for x =...
7. Let X and Y have joint probability mass function fx.y(x,y) = (x+y)/30 for x = 0.1, 2.3 and y0,1,2. Find (a) PrX 2,Y-1) (b) PrX>2,Y S1) (c) Pr(X + Y=4) (d) Pr[X >Y) (e) the marginal probability mass function of Y, and (f) E[XY]
Let X and Y have joint probability mass function fX,Y (x, y) = (x + y)/30 for x = 0, 1, 2, 3 and y = 0,1,2. Find: (a) Pr{X ≤ 2, Y = 1}(b) Pr{X > 2, Y ≤ 1} (c) Pr{X +Y = 4}. (d) Pr{X > Y }. (e) the marginal probability mass function of Y , and (f) E[XY].
Let X and Y have joint probability density function fx,y(x,y) = e-(z+y) for 0 x and 0 y. Find (a) Pr(X=y (b) Prmin(X, Y) > 1/2) (c) Pr(X Y) d) the marginal probability density function of Y (e) E[XY].
Let X and Y be continuous random variables with joint pdf f(x,y) =fX (c(X + Y), 0 < y < x <1 otBerwise a. Find c. b. Find the joint pdf of S = Y and T = XY. c. Find the marginal pdf of T. 、
Consider fx (x)=e*, 0<x and joint probability density function fx (x, y) = e) for 0<x<y. Determine the following: (a) Conditional probability distribution of Y given X =1. (b) ECY X = 1) = (c) P(Y <2 X = 1) = (d) Conditional probability distribution of X given Y = 4.
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].
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).
7. The random variables X and Y have joint probability density function f given by 1 for x > 0, |y| 0 otherwise. 1-x, Below you find a diagram highlighting the (r, y) pairs for which the pdf is 1 (a) Calculate the marginal probability density function fx of X (b) Calculate the marginal cumulative distribution function Fy of Y (c) Are X and Y independent? Explain.
7. The random variables X and Y have joint probability density function f given by 1 for x > 0, |y| 0 otherwise. 1-x, Below you find a diagram highlighting the (r, y) pairs for which the pdf is 1 (a) Calculate the marginal probability density function fx of X (b) Calculate the marginal cumulative distribution function Fy of Y (c) Are X and Y independent? Explain.
< 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).