If X and Y have a joint density given by f(x, y) = 2, for 0 < y < x < 1 0, elsewhere (a) If V = −lnX, what is the density of V ? (b) If V = −lnX and W = X + Y , what is the joint density of V and W? Sketch the region for which the joint density is nonzero.
[2.5 points] If two random variables have a joint density given by, f(x, y) = k(3x + 2y) 0 for 0 < x < 2, 0 < y < 1 elsewhere (a) Find k (b) Find the Marginal density of Y. (c) Find E(Y) (d) Find marginal density X. (e) Find the probability, P(X < 1.3). (f) Evaluate fı(x|y); (g) Evaluate fi(x|(0.75))
the answer should be 1/2 +x 4. Let X and Y joint density function ( 2e-2(x+y) if 0<r<y< f(x,y) = elsewhere. What is the expected value of Y, given X = x, for x > 0?
4. Let X and Y have joint density function le-x 0 < y < x < 0 Jxy(x, y) = lo elsewhere Another random variable of interest is U=X–Y. Find the probability density function for U.
Let (X,Y) have joint pdf given by f(x, y) = { Sey, 0 < x <y<, | 0, 0.W., (a) Find the correlation coefficient px,y (b) Are X and Y independent? Explain why.
Let (X,Y) have joint pdf given by sey, 0 < x < y < 0, f(x, y) = { ( 0, 0.W., (a) Find the correlation coefficient px,y: (20 pts) (b) Are X and Y independent? Explain why. (10 pts)
# 6 If two random variables have the joint density f(x, y)=59 y?) for 0<x<1, 0<y<1 0 elsewhere a. Find the probability that 0.2 X<0.5 and 0.4<Y<0.6. b. Find the probability distribution function F(x, y). c. Are x and y independent?
2nd pic is answer. show the work plz 13 Let X and Y have the joint probability density function ,흄.ru2 for 0 < x < y. < 2 f(x,y) = elsewhere What is the joint density function of U it is nonzero? 3X-2Y and V-X + 2Y where 687 Probability and Mathematical Statistics 32768 13° g(u,t) = 0 otherwise.
3. Suppose X and Y have joint density f(x,y)- "cy. 0 < x < y < oo, and equal to 0 for all other (r, y). (a) Calculate the joint density of U = Y-X,V-X. (b) Are U and V independent?
(1 point) The joint probability density function of X and Y is given by f(x, y) = cx – 16 c”, - <x< 0 < b < co alt 0 < y < 0 Find c and the expected value of X: c = E(X) =