1. (20 pts) RVs X and Y have joint density function 22 f(x, y) =(0 if O <z<1 and 0<y<2 īf 0 < x < 1 and 0 < y < 2 otherwise (a) Find E(X), V(X), E(Y), and V(Y). (b) Find t...
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...
f(x,y) = K(x^2 + y^2) in 0 < x < 1, 0 < y < 1 Determine the value of the constant that makes a joint density function. (a) Find fx(X) (b) Find fy(Y) (a) Find E(X) (b) FindE(Y) (a) Find V(X) (b) Find V(Y) Find the covariance cov(X,Y) Interpret your result.
[15] 5. (X, Y) have joint density (22 + y?) 0<*<1 0<y<1 f(x, y) else find the marginals fx(x) and fy (y).
Suppose X andY have joint density f(x,y)=6*x*y^2 for 0<x<1, 0<y<1. (a) What is P(X+Y ≤1)? (b) Compute the marginal densities fX , fY of X, Y .
The joint pdf of two continuous RVs X and Y is given by (4e-22–24 0 < x,y< f(x, y) = { otherwise Then cov(X,Y) equals Hint – Think of the exponent identity eath = eeb and how this can be used to factorize or simplify joint pdf. OO 0.28 0 -0.46 O 0.83 1
The joint probability density function of the random variables X, Y, and Z is (e-(x+y+z) f(x, y, z) 0 < x, 0 < y, 0 <z elsewhere (a) (3 pts) Verify that the joint density function is a valid density function. (b) (3 pts) Find the joint marginal density function of X and Y alone (by integrating over 2). (C) (4 pts) Find the marginal density functions for X and Y. (d) (3 pts) What are P(1 < X <...
The joint density function of the continuous variables X and Y is fX,Y(x,y) = (12/5)*x*(2-x-y) for 0<X<1 and 0<Y<1. a) Find the expected value of X+Y. (b) Find fX(x), and fY(y). (c) Find Cov(X,Y). (d) Find Corr(X,Y).
Consider the random variables X and Y with joint density function [5] f(x,y)=1/x , 0<y<x<1 i) Find P(X > 0 . 5 , y >0.5). ii) Find fX | y(x) and fY | x(y)..
0/1 point (graded X, Y have the joint probability density function f (z,y)-1 , 0 < z < 1, z < y < z + 1 . Please enter a number. Cov (X,Y) SubmitYou have used 2 of 3 attempts Save Incorrect (O/1 point) 1 point possible (graded) x ~ f(z) 2be-HA, z є R, b > 0 and Y-sign (X) Cov (X, Y)- SubmitYou have used 0 of 3 attempts Save We were unable to transcribe this image 0/1...