Joint Density

Find the conditional distribution of Y given X = ... (Joint density of X and Y given) *(Please see attachment for complete problem)

Let X and Y have the joint pdf f x,y(X,Y) = 2e^(-(x+y)) , 0

3. The joint probability density function of X and Y is given by f(x, y) =6/7 (x2 + xy/2 ), 0 < x < 1, 0 < y < 2. (a) Verify that this is indeed a joint density function. (b) Compute the density function of X. (c) Find P(X > Y ). (d) Find P(Y > 1/2|X < 1/2). (e) Find E(X). (f) Find E(Y ). Please see attachment for

4.17. X has the U(?pi/2, pi/2) distribution, and Y = tan(X). Show that V has density l/(pi(1 + y2)) for ?oo density function.) What can be said about the mean and variance of Y? How could you simulate values from this distribution, given a supply of U(O, 1) values? 4.21. Let X and Y have joint den

Determine the value of c that makes the function f(x,y) = c(x+y) a joint probability density function over the range: x greater than 0 and less than 3 and x less than y less than x+2 a) P(X<1, Y<2) b) P(11) d) P(X<2, Y<2) e) E(X) f) V(X) g) Marginal probability distribution of X h) Conditional probabilit

Let X, Y be independent, standard normal random variables, and let U = X + Y and V = X - Y. (a) Find the joint probability density function of (U, V) and specify its domain. (b) Find the marginal probability density function of U and V specifying the domain in each case. (c) Explain why U and V are independent Joint probab

Please see the attached file for the fully formatted problems. Y1 & Y2 denotes the proportions of time that employee I and II actually spent working on their assigned tasks during a workday. The joint density of Y1 & Y2 is given by: f(y1,y2) = y1 + y2 , 0=

Two different problems below: #1.) The following is the joint density for two random variables, X1 and X2: f(X1, X2): {3X1 for 0<=X2<=X1<=1 0 elsewhere Find P(0.2<=X2<=0.4) Which of the following answers: a.) 0.3750 b.) 0.2720 c.) 0.1800 d.) 0.3(1- X

A fair coin is tossed four times and X is number of heads on first three tosses and Y on last three. What is the joint probability mass function of x and y? What is the marginal pmf? Are X and Y independent?