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).

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
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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 :

λ1=2,λ2=3

Poisson Distribution :

P(X=x)=λxe-λx!P(X = x) = Probability of exactly (x) occurrences in a given intervalλ  = mean number of occurrences during intervalX = number of occurrences desirede = base of the natural logarithm

 

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