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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

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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}
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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