8. Let X and Y be a random variable with joint continuous pdf: f(x,y)- 0< y...
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. 、
Let X and Y be random variables with joint PDF fx,y(x, y) = 2 for 0 < y < x < 1. Find Var(Y|X).
1. Suppose X and Y are continuous random variables with joint pdf f(x,y) 4(z-xy) if = 0 < x < 1 and 0 < y < 1, and zero otherwise. (a) Find E(XY) b) Find E(X-Y) (c) Find Var(X - Y) (d) What is E(Y)?
Let X and Y be continuous random variables with following joint pdf f(x, y): y 0<1 and 0<y< 1 0 otherwise f(x,y) = Using the distribution method, find the pdf of Z = XY.
2. Let X and Y be continuous random variables having the joint pdf f(x,y) = 8xy, 0 <y<x<1. (a) Sketch the graph of the support of X and Y. (b) Find fi(2), the marginal pdf of X. (c) Find f(y), the marginal pdf of Y. () Compute jx, Hy, 0, 0, Cov(X,Y), and p.
Let X and Y be continuous random variables with joint pdf fx.v (x, y)-3x, OSysx<1, and zero otherwise. a. b. c. d. e. What is the marginal pdf of X? What is the marginal pdf of Y? What is the expectation of X alone? What is the covariance of X and Y? What is the correlation of X and Y?
8), Let X and Y be continuous random variables with joint density function f(x,y)-4xy for 0 < x < y < 1 Otherwise What is the joint density of U and V Y
Let X and Y be continuous random variables with joint distribution function: f(x,y) = { ** 0 <y < x <1 otherwise What is the P(X+Y < 1)?
LI CONTINUOUS DIST Let X be a random variable with pdf -cx, -2<x<0 f(x)={cx, 0<x<2 otherwise where c is a constant. a. Find the value of c. b. Find the mean of X. C. Find the variance of X. d. Find P(-1 < X < 2). e. Find P(X>1/2). f. Find the third quartile.
5. Y is a continuous random variable with pdf f(y) = (4 – y)/8, 0<y< 4. (a) Find E(Y). (b) Find E(Y2). (c) Find Var(Y).