Ans is 1/6 or 0.1667
13. (8 pts.) Two random variables have the following pdf fxr(x, y) = {fx (1 –...
13. (8 pts.) Two random variables have the following pdf fxx (x, y) = {4x(1–» (4x(1 - y),0 < x <1,0 < y < 1 0, otherwise Find P[X<Y] 14. We are interested in the average escape time for firemen participating in a drill that involves escaping a dangerous situation. A random sample of 26 escape times is taken and gives a mean of 24.36 with a variance of 370.69. We wish to find a 95% confidence interval for the...
4) The random variables X and Y have the joint PDF fx,y(x, y) = 0 < x < 6,0 < y < 6 Find E [X2Y2].
Let X and Y be random variables with joint PDF fx,y(x, y) = 2 for 0 < y < x < 1. Find Var(Y|X).
7. The joint pdf of two random variables X and Y is given by 0sxs3,0s y<5 fx(x,y) 15' 0, otherwise Find Cov(X,y)
7.5.6 Random variables X and Y have joint PDF fx,y(x, y) = _J1/2 -1 < x <y <1, 1/2 10 otherwise. (a) What is fy(y)? (b) What is fx|v(x\y)? (c) What is E[X|Y = y)?
Let X, Y be jointly continuous with joint density function (pdf) fx,y(x, y) *(1+xy) 05 x <1,0 <2 0 otherwise (a) Find the marginal density functions (pdf) fx and fy. (b) Are X and Y independent? Why or why not?
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. 、
Suppose X, Y are random variables whose joint PDF is given by fxy(x,y) = { 0<y<1,0<=<y 0, otherwise 1. Find the covariance of X and Y. 2. Compute Var(X) and Var(Y). 3. Calculate p(X,Y)
7. Suppose the random variables (X, Y) have joint pdf given by Ta ſ cx2y2 if 0 <x sys1, l o otherwise. a. Find the constant c. b. Find the marginal density of X. c. Find the marginal density of Y. d. Are X and Y independent?
2. Let the random variables X and Y have the joint PDF given below: S 2e-2-Y 0 < x < y < fxy(x,y) = { 0 otherwise (a) Find P(X+Y < 2). (b) Find the marginal PDFs of X and Y. (c) Find the conditional PDF of Y|X = r. (d) Find P(Y <3|X = 1).