hw1prob2 - Homework Assignment 1 Queuing Theory: 56 645558...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Homework Assignment 1 Queuing Theory: 56 645558 01 Problem 2 - Sum of Random Variables Tony Smaldone [email protected] http://www.sntco.com/tony/masters.html July 26, 2001 Problem 2 - Sum of Random Variables Find the distribution (density) of Y = X 1 + X 2 for the two cases where a). X 1 Poisson ( λ 1 ) and X 2 Poisson ( λ 2 ) ; and, b). X 1 Exp ( λ 1 ) and X 2 Exp ( λ 2 ) . Assume independence. Solution a). Poisson Distribution Given two independent random variables X 1 Poisson ( λ 1 ) and X 2 Poisson ( λ 2 ) the question becomes what is the distribution of Y = X 1 + X 2 . Since X 1 and X 2 are independent events, the distribution of Y will be the sum of all possible values of X 1 and X 2 which sum to Y . For example, if P [ Y = k ], then P [ Y = k ] = P [ X 1 = 0] P [ X 2 = k ] + P [ X 1 = 1] P [ X 2 = k - 1] + ··· + P [ X 1 = k ] P [ X 2 = 0] = k X n =0 P [ X 1 = n ] P [ X 2 = k - n ] Expanding the summation k n =0 P [ X 1 = n ] P [ X 2 = k - n ] 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
= e
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/05/2010 for the course ECE 01 taught by Professor All during the Spring '09 term at Aarhus Universitet.

Page1 / 3

hw1prob2 - Homework Assignment 1 Queuing Theory: 56 645558...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online