and answer is:
However, how do you find the integral boundaries of G(z), and how do you find the interval of g(y) [ -1 <= z <= 1 ]
and answer is: However, how do you find the integral boundaries of G(z), and how do you find the interval of g(y) [ -1 <= z <= 1 ] 3(x + y), x-1 1-x,0 1 y zero, otherwise x roP+27 vx.151 A jo...
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?
Question 1(a&b)
Question 3 (a,b,c,d)
QUESTION 1 (15 MARKS) Let X and Y be continuous random variables with joint probability density function 6e.de +3,, х, у z 0 otherwise f(x, y 0 Determine whether or not X and Y are independent. (9 marks) a) b) Find P(x> Y). Show how you get the limits for X and Y (6 marks) QUESTION 3 (19 MARKS) Let f(x, x.) = 2x, , o x, sk: O a) Find k xsl and f(x,...
2. Let the joint probability density function of (X, Y) be given by {ay otherwise. 1 and 0 < y < 2, f(z,y) (a) [6 pts] Determine if X and Y are independent. (b) [6 pts] Find P{X+Y <1) B( (c) [6 pts) Find
2. Let the joint probability density function of (X, Y) be given by {ay otherwise. 1 and 0
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...
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...
Problem 2 - Three Continuous Random Variables Suppose X,Y,Z have joint pdf given by fx,YZ(xgz) = k xyz if 0 S$ 1,0 rS 1,0 25 1 ) and fxyZ(x,y,z) = 0, otherwise. (a) Find k so that fxyz(x.yz) is a genuine probability density function. (b) Are X,Y,Z independent? (c) Find PXs 1/2, Y s 1/3, Z s1/4). (d) Find the marginal pdf fxy(x.y). (e) Find the marginal pdf fx(x).
Problem 2 - Three Continuous Random Variables Suppose X,Y,Z have joint...
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 the covariance cov(X,Y) and the associated correlation ρ (c) Find the marginal densities fx and fy. (Be sure to say where they're nonzero.) (d) Find E(X | Y = 1.5). (e) Are X and Y independent? Give two...
4. The joint distribution of X and Y is given by 0 otherwise (a) Are X and Y independent? Explairn. (b) Find the marginal probability function (pdf) of Y, fy (). (c) Provide the integral for finding P(X < Y), but DO NOT evaluate.
Plz help me to do both quetions.
6. The continuous random variables X and Y have joint density 2e2)for and y 20 otherwise Find P(X >Y). (Answer: 3) 7. The continuous random variables X and Y have joint probability density function 10y for 01 and 0 yr fzy(z,y)=ï o otherwise Find the marginal density function fy(y). Show your work. Do not forget to indicate where the density is non-zero.
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 <...