There are 60 infections in village A per month and 48 infections in village B per month.(adsbygoogle = window.adsbygoogle || []).push({});

Let A be no of infections in village A per month and B be no of infections in village B per month. Assume occurrence is independent and random.

So

Method 1 (Working method):

A~Po (60) and B~Po (48)

Using a suitable approximation, find the probability that in 1 month, the no of infections in B exceeds no of infections in A.

Since λ>10, A~ N(60,60) and B~N(48,48) approximately

B-A~(-12, 108)

P(B>A)=P(B-A>0)=0.115

This I can understand but when I tried another method, it didnt work.

Method 2: Through linear combination of poisson (???Cannot get it to work???)

A-B ~ Po(12)

Since λ>10, A-B~N(12,12)

P(A<B)=P(A-B<0)=2.66x10^{-4}

Why the difference? Why does the second method not work?

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# Poisson Approximation

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