Problem 1: Given the function g(x,y)-ke-xy-c)u(x-a)u(y-b) find the constant "k" in terms ofa, b, and c...
Find a constant k (in terms of a) so that the function fxx (x,y) = e-(x+u) 0 << oo and 0 < y <a and O elsewhere is a valid joint density function.
4.3-8 (a) Find a constant b (in terms of a) so that the functionomit o ovi tbe be x+y) 0<x<a and Assum Problem 0<y< fx.y(x, y)= Work Proble elsewhere is a valid joint density function. nt ob lanigu (b) Find an expression for the joint distribution function. d oninst () 4.2-10. Discrete random variables X and Y have a joint distribution function Fx.y(x,y) 0.10u(x+4)u(y-1)+0.15u(x +3)u(y+5) +0.17u(x+1)u(y-3) +0.05u(x)u(y-1) +0.18u(x-2)u(y + 2) + 0.23u(x-3)u(y-4) +0.12u(x-4)u(y +3) Dete
The joint PDF of random variables X and Y is expressed as
(a) Determine the constant c.
(b) Determine the marginal density function for X.
(c) Determine the marginal density function for Y.
(d) Are X and Y statistically independent?
(e) Determine the probability of P(X ≤ 0.5 | Y = 1).
The joint PDF of random variables X and Y is expressed as certy, 05xs1 and 05ys2 fx.x(x, y) = 10. elsewhere. (a) Determine the constant c. (b) Determine...
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...
random vibrations
Problem 1 Two random variables x and y have the joint probability density function where c is a constant. Verify that x and y are statistically independent and find the value of c for plx, y) to be correctly normalized. Check that Elx) Elyl-0 and that Elx2] and Ely') are both infinite Problem 2. Each sample function x(t) of a random process x(t) is given by: where a, a2, wh, and w are constants but 61 and 62,...
1. Consider two random variables X and Y with joint density function f(x, y)-(12xy(1-y) 0<x<1,0<p<1 otherwise 0 Find the probability density function for UXY2. (Choose a suitable dummy transformation V) 2. Suppose X and Y are two continuous random variables with joint density 0<x<I, 0 < y < 1 otherwise (a) Find the joint density of U X2 and V XY. Be sure to determine and sketch the support of (U.V). (b) Find the marginal density of U. (c) Find...
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 =...
Consider random variables X and Y with joint probability density function (Pura s (xy+1) if 0 < x < 2,0 <y S4, fx.x(x, y) = otherwise. These random variables X and Y are used in parts a and b of this problem. a. (8 points) Compute the marginal probability density function (PDF) fx of the random variable X. Make sure to fully specify this function. Explain.