3. Joint density of X and Y is given by otherwise Find k and P(x Y...
Let X and Y have joint density xY)0otherwise. 0 otherwise (a) Find k. (b) Compute the marginal densities of X and of Y (c) Compute P(Y 2x). (d) Compute P(X-Y| 〈 0.5). (e) Are X and Y independent?
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...
7. Given the joint density function /(x,y) =(kx (1 + 3 y*) 0<x<2,0<p?1 elsewhere a. Find k, g() h) and f(x) b. Evaluate P(-<X<1)
. The joint density of the random variables X and Y is given as c f(x,y) = 1 < x <y <3 otherwise 10, i) Find c such that f(x,y) is a valid density function. ii) Set up the calculation for P(X<2, Y> 2). You do not need to compute this value. iii) Find the marginal distribution of X and the marginal distribution of Y.
2. Let the joint probability density function of (X, Y) be given by {ay otherwise. 1 and 0 < y < 2, f(z,y) (a) [6 pts] Determine if X and Y are independent. (b) [6 pts] Find P{X+Y <1) B( (c) [6 pts) Find
2. Let the joint probability density function of (X, Y) be given by {ay otherwise. 1 and 0
6. The joint density of the random variables X and Y is given as F. ( 1 <rsy <3 otherwise i) Find e such that is a valid density function.(8 pts) ii) Set up the calculation for P(X 2.Y > 2). You do not need to compute this value. (5 pts) iii) Find the marginal distribution of X and the marginal distribution of Y. (14 pts) iv) Find E(X) and E(Y)(10 pts) Find ox and of (18 pts) vi) Find...
Q1. Let X and Y have joint density 0, otherwise. a. Find the marginal densities of X and Y b. Find P(0.2 < Y < 0.31X = 0.8).
and y Problem 93.) Joint Density of Random vanable Сут- < X<Y <3 O otherwise ) c Such that Sex,y) is Valid density a function 6.) How would you calculate P(x = 2, Y > Z) + Find Marginal distribution of x Marginal distribution of y d.) Find both E(X) + E(y) and on to y
(8pts) 1. The joint probability density of X and Y is given by + 0<x<1 and 0 <y< 2 otherwise a) Verify that this is a joint probability density function. b) Find P(x >Y). o) Find Pſy > for< d) Find Cov(X,Y). e) Find the correlation coefficient of X and Y (Pxy).
8. Suppose that the joint density of X and Y is given by e if 0< I<, 0<y< 0, otherwise. Find P(X > 1 Y = y).