5. Let the joint probability density function of X and Y be given by, f(x,y) =...
5. Let X and Y have joint probability density function of the form Skxy if 0 < x +y < 1, x > 0 and y > 0, f(x,y)(, y) = { 0 otherwise. (a) What is the value of k? (b) Giving your reasons, state whether X and Y are dependent or independent. (c) Find the marginal probability density functions of X and Y. (d) Calculate E(X) and E(Y). (e) Calculate Cov(X,Y). (f) Find the conditional probability density function...
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...
1. Let X and Y have the joint density function given by zob to todos f(x, y) = {kxy) of 50<x< 2, 0 <y<3.) i 279VHb yodmu : 1093 otherwise a) Find the value of k that makes this a probability density function. TO B 250 b) Find the marginal distribution with respect to y. 0x11 sono c) Find E[Y] d) Find V[Y]. X10 sulay boso 50
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
Let X and Y be jointly continuous random variables with joint probability density given by f(x, y) = 12/5(2x − x2 − xy) for 0 < x < 1, 0 < y < 1 0 otherwise (a) Find the marginal densities for X and Y . (b) Find the conditional density for X given Y = y and the conditional density for Y given X = x. (c) Compute the probability P(1/2 < X < 1|Y =1/4). (d) Determine whether...
Let X and Y be jointly continuous random variables with joint probability density given by f(x, y) = 12/5(2x − x2 − xy) for 0 < x < 1, 0 < y < 1 0 otherwise (a) Find the marginal densities for X and Y . (b) Find the conditional density for X given Y = y and the conditional density for Y given X = x. (c) Compute the probability P(1/2 < X < 1|Y =1/4). (d) Determine whether...
5. Let the joint cumulative density function of random variables X and Y be given by for z 0, y >0. (Note: Fxy(x, y)-0 outside this domain.) (a) Find P(X S2,Y (b) Find P(X5). (c) Find P(2 <Y s6). (d) Find the joint probability density function f(x, y). Show that your answer satisfies the S 2). two defining properties of a density. (e) Are X and Y independent? Why or why not?
The joint probability density function of random variables X and Y is given by f(x,y) ={10xy^2 0≤x≤y≤1,0 otherwise. (a) Compute the conditional probability fX|Y(x|y). (b) Compute E(Y) and P(Y >1/2). (c) Let W=X/Y. Compute the density function of W. (d) Are X and Y independent? Justify briefly.
2. Suppose that (X,Y) has the following joint probability density function: f(x,y) = C if -1 <r< 1 and -1 <y<1, and 0 otherwise. Here is a constant. (a) Determine the value of C. (b) Are X and Y independent? (Explain why or why not.) (c) Calculate the probability that 2X - Y > 0 (d) Calculate the probability that |X+Y| < 2 3. Suppose that X1 and X2 are independent and each is standard uniform on (0,1]. Let Y...
7. The random variables X and Y have joint probability density function f given by 1 for x > 0, |y| 0 otherwise. 1-x, Below you find a diagram highlighting the (r, y) pairs for which the pdf is 1 (a) Calculate the marginal probability density function fx of X (b) Calculate the marginal cumulative distribution function Fy of Y (c) Are X and Y independent? Explain.