12) Assume that the following function f(x,y) is the joint distribution density function for X and...
Assume that the joint density function of X and Y is given by f (x, y) = 4,0 < x < 2,0 < y = 2 and f (x, y) = 0 elsewhere. (a) Find P (X < 1, Y > 1). (b) Find the joint cumulative distribution function F(x, y) of the two random variables. Include all the regions. (c) Find P (X<Y). (d) Explain how the value of P (1 < X < 2,1 < Y < 2)...
The joint density function of X and Y is J x +y if 0 < x,y<1 f(x, y) = 3. otherwise. a) Are X and Y independent? b) Find the density of X. c) Find P(X + Y < 1).
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...
. The joint density of the random variables X and Y is given as c f(x,y) = 1 < x <y <3 otherwise 10, i) Find c such that f(x,y) is a valid density function. ii) Set up the calculation for P(X<2, Y> 2). You do not need to compute this value. iii) Find the marginal distribution of X and the marginal distribution of Y.
5. Let the joint probability density function of X and Y be given by, f(x,y) = 0 otherwise (a) Find the value of A that makes f (x, y) a proper probability density function (b) Calculate the correlation coefficient of X and Y. (c) 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.
The joint probability density function for continuous random variables X and Y is given below. f (x) = x + y, 0 < x < 1, 0 < y < 1 if; 0, degilse. (a) Show that this is a joint density function. (b) Find the marginal density of X . (c) Find the marginal density of Y . (d) Given Y = y find the conditional density of X . (e) P ( 1/2 < X < 1|Y =...
The joint probability density function for continuous random variables X and Y is given below. f (x) = x + y, 0 < x < 1, 0 < y < 1 if; 0, degilse. (a) Show that this is a joint density function. (b) Find the marginal density of X . (c) Find the marginal density of Y . (d) Given Y = y find the conditional density of X . (e) P ( 1/2 < X < 1|Y =...
The joint probability density function for continuous random variables X and Y is given below. f (x) = x + y, 0 < x < 1, 0 < y < 1 if; 0, degilse. (a) Show that this is a joint density function. (b) Find the marginal density of X . (c) Find the marginal density of Y . (d) Given Y = y find the conditional density of X . (e) P ( 1/2 < X < 1|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.