Answered: Let X1 and X2 be independent Poisson…

Let X1 and X2 be independent Poisson random variables with respective means lambda1 = 2 and lambda2 = 3. Find (a) P(X1=3,X2=5). (b) P(X1 + X2 = 1).

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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Question

Let X1 and X2 be independent Poisson random variables with respective means lambda1 = 2 and lambda2 = 3.

Find

(a) P(X1=3,X2=5).

(b) P(X1 + X2 = 1).

Expert Solution

Step 1

From given data we have :

$λ_{1} = 2, λ_{2} = 3$

Poisson Distribution :

$P (X = x) = \frac{λ^{x} e^{- λ}}{x!} P(X = x) = Probability of exactly (x) occurrences in a given interval λ = mean number of occurrences during interval X = number of occurrences desired e = base of the natural logarithm$

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