Homework 1- The joint probability density function of random variables (X,Y) is given by: fxy(x,y) = {k(x+y) 0
Homework 1- The joint probability density function of random variables (X,Y) is given by: fxy(x,y) = {k(x+y) 0
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 23E
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![Homework
1- The joint probability density function of random variables (X,Y) is given by:
fxv (x, y) = {*(x + y
0 <x < 2, 0 < y< 2
other wise
Where k is constant.
Find:
(a) The value of k {ans: k=1/8}
(b) The marginal density functions of X and Y
(x+1)
o+1)
0<y < 2;
0 <x< 2
{ans: fx(x) = .
fy (y) =
other wise
other wise
(c) fxjy (x\y) and frxVlx)
x+y
0 < x < 2, 0 <y<2
{ans: fxjy(x|y) = {2(y+1)
other wise
x+y
0 <x< 2, 0 <y<2
fyix(y]x) = {2(x+1)
other wise
(d) Are X and Y independent and why? {ans:NO}
(e) Fxy(1,1.5) {ans: 0.2343}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8ba548b9-f64d-4c97-bd53-4538a63517e0%2F367d66cf-6757-4dd9-9a35-477e1bd802ef%2Fxdxj03h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Homework
1- The joint probability density function of random variables (X,Y) is given by:
fxv (x, y) = {*(x + y
0 <x < 2, 0 < y< 2
other wise
Where k is constant.
Find:
(a) The value of k {ans: k=1/8}
(b) The marginal density functions of X and Y
(x+1)
o+1)
0<y < 2;
0 <x< 2
{ans: fx(x) = .
fy (y) =
other wise
other wise
(c) fxjy (x\y) and frxVlx)
x+y
0 < x < 2, 0 <y<2
{ans: fxjy(x|y) = {2(y+1)
other wise
x+y
0 <x< 2, 0 <y<2
fyix(y]x) = {2(x+1)
other wise
(d) Are X and Y independent and why? {ans:NO}
(e) Fxy(1,1.5) {ans: 0.2343}
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