7. Let X and Y have joint probability mass function fx.y(x,y) = (x+y)/30 for x =...
7. Let X and Y have joint probability mass function fx,y(x,y) = (z+y)/30 for x = 0, 1, 2, 3 and y-0,1,2. Find (a) Pr(X 2, Y=1} (b) PríX > 2, Y 1) (c) PrXY-4) (d) PrX>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 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].
The random variable X and Y have the following joint probability mass function: P(x,y) 23 0.2 0.1 0.03 0.1 0.27 0 4 0.05 0.15 0.1 a) Determine the marginal pmf for X and Y. b) Find P(X - Y> 2). c) Find P(X S3|Y20) e Determine E(X) and E(Y). f)Are X and Y independent?
. For > 0 and A > 0, define the joint pdf -Ay = 0<x<A,<y, fx.y(,y) 10 else. (a) Express c in terms of X and A. (b) Find E[XY]. (c) Let [2] be the largest integer less than or equal to z. For example, (3.2] = 3 and [2] = 2. Find the probability that [Y] is even, given that 4 <x< 34
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.
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].
< 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).
55. Let X and Y be jointly continuous random variables with joint density function fx.y(x,y) be-3y -a < x < 2a, 0) < y < 00, otherwise. Assume that E[XY] = 1/6. (a) Find a and b such that fx,y is a valid joint pdf. You may want to use the fact that du = 1. u 6. и е (b) Find the conditional pdf of X given Y = y where 0 <y < . (c) Find Cov(X,Y). (d)...