Suppose X and Y have joint probability density function
fX,Y(x,y)=70e?3x?7y |
for 0<x<y; and fX,Y(x,y)=0 otherwise. Find E(X). (You may either use the joint density given here,
Suppose X and Y have joint probability density function fX,Y(x,y)=70e?3x?7y for 0<x<y; and fX,Y(x,y)=0 otherwise. Find...
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...
(3x, The joint density function of X and Y is given by 0 Sy sxs1 f(x, y) = 0, otherwise. a) Use the distribution function technique to find the distribution function of W = X-Y. For 50% of the points, you may use the transformation technique, which is longer. >) Find the probability density function of W. Find the expected value E(W). )
Q.4 (22') Suppose the joint probability density function of X and Y is fx,y(x, y) = { „) - k(2 - x + y)x 0 sxs 1,0 sys1 o otherwise (a) (7”) Show that the value of constant k = 12 (b) (7') Find the marginal density function of X, i.e., fx(x). (c) (8') Find the conditional probability density of X given Y=y, i.e., fxy(xly). 11
4. The random variables X and Y have joint probability density function fx,y(x, ) given by: fx,y(x, y) 0, else (a) Find c. (b) Find fx(x) and fy (), the marginal probability density functions of X and Y, respectively (c) Find fxjy (xly), the conditional probability density function of X given Y. For your limits (which you should not forget!), put y between constant bounds and then give the limits for in terms of y. (d) Are X and Y...
Problem 5. The joint density of X and Y is given by e" (z+y) fx.-otherwise. İf 0 < x < oo, 0 < y < 00, Consider the random variable Z-; a) Find the cumulative distribution function of Z b) What is the probability density function of Z?
Let X and Y have joint probability density function fX,Y (x, y) = e−(x+y) for 0 ≤ x and 0 ≤ y. Find: (a) Pr{X = Y }. (b) Pr{min(X, Y ) > 1/2}. (c) Pr{X ≤ Y }. (d) the marginal probability density function of Y . (e) E[XY].
1. Consider the joint probability density function 0<x<y, 0<y<1, fx.x(x, y) = 0, otherwise. (a) Find the marginal probability density function of Y and identify its distribution. (5 marks (b) Find the conditional probability density function of X given Y=y and hence find the mean and variance of X conditional on Y=y. [7 marks] (c) Use iterated expectation to find the expected value of X [5 marks (d) Use E(XY) and var(XY) from (b) above to find the variance of...
Consider fx (x)=e*, 0<x and joint probability density function fx (x, y) = e) for 0<x<y. Determine the following: (a) Conditional probability distribution of Y given X =1. (b) ECY X = 1) = (c) P(Y <2 X = 1) = (d) Conditional probability distribution of X given Y = 4.
Q. Suppose the joint probability density function of X and Y is (a) Show that the value of constant ?=12/11 (b) Find the marginal density function of X, i.e., fX(x). (c) Find the conditional probability density of X given Y = y, i.e., fX|Y(x|y). fxy(x, y) = s k(2 - x + y)x 1 0 0 < x < 1,0 = y = 1 otherwise
4. Let X and Y have joint probability density function f(x,y) = 139264 oray3 if 0 < x, y < 4 and y> 4-1, otherwise. (a) Set up but do not compute an integral to find E(XY). (b) Let fx() be the marginal probability density function of X. Set up but do not compute an integral to find fx(x) when I <r54. (c) Set up but do not compute an integral to find P(Y > X).