4.3-17. Find the marginal densities of X and Y using the joint density Sx.x(x,y) = 2u(x)u(v)exp-...
Q1. Let X and Y have joint density 0, otherwise. a. Find the marginal densities of X and Y b. Find P(0.2 < Y < 0.31X = 0.8).
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 random variables X and Y are independent with exponential densities fx (x) = e-"u(x) (a) Let Z = 2X + and w =-. Find the joint density of random variables Z and W (b) Find the density of random variable W (c) Find the density of random variable Z The random variables X and Y are independent with exponential densities fx (x) = e-"u(x) (a) Let Z = 2X + and w =-. Find the joint density of random...
Let X and Y have joint density Jxy(Cr,9)0otherwise. (a) Compute the marginal densities of X and Y. (b) Compute P(y 〉 2X). (c) Are X and Y independent?
Comparing two densities. Joint density (a) for random variables X and Y is given by: fxy(x, y) = 6e-23-if 0 <y<I<0. Joint density (b) for random variables X and Y is given by: fxY(I, y) = 2e -2- if 0 <1,7 <00. Fill in the following chart and determine whether or not X and Y are independent for both densities (a) and (b). fx() fy(y) EX EY EXY Cou(X,Y) Independent?
1. Suppose that the joint density of X and Y is given by exp(-y) (1- exp(-x)), if 0 S y,0 syS oo exp(-x) (1- exp(-y)), if 0SyS ,0 oo (e,y)exp(-y) Then . The marginal density of X (and also that of Y), ·The conditional density of Y given X = x and vice versa, Cov(X, Y) . Are X and Y independent? Explain with proper justification.
Suppose the joint density of (X, Y ) is: fX,Y (u, v) = u + v for 0 ≤ u, v ≤ 1, and 0 otherwise. Compute the marginal density of X. compute E(X) and Var(X)
1. Suppose that the joint density of X and Y is given by exp(-y) (1- exp(-x)), if 0 S y,0 syS oo exp(-x) (1- exp(-y)), if 0SyS ,0 oo (e,y)exp(-y) Then . The marginal density of X (and also that of Y), ·The conditional density of Y given X = x and vice versa, Cov(X, Y) . Are X and Y independent? Explain with proper justification. 1. Suppose that the joint density of X and Y is given by exp(-y)...
55. Let X and Y be jointly continuous random variables with joint density function fx.y(x,y) be-3y -a < x < 2a, 0) < y < 00, otherwise. Assume that E[XY] = 1/6. (a) Find a and b such that fx,y is a valid joint pdf. You may want to use the fact that du = 1. u 6. и е (b) Find the conditional pdf of X given Y = y where 0 <y < . (c) Find Cov(X,Y). (d)...
2. Let X and Y be two continuous random variables varying in accordance with the joint density function, fx.y(z, y-e(x + y) for 0 < z < y < 1. Solve the following problem s. (1) Find e, fx(a) and fy (v) (2) Find fx-u(z) and fY1Xux(y) (8) Find P(Y e (1/2, 1)|X -1/3) and P(Y e (1/2,2)| X 1/3). 3. Find P(X < 2Y) if fx.y(zw) = x + U for X and Y each defined over the unit...