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Recurrence relationship in negative binomial and poison distribution & Study mates

A

Ashih Folo

Member
Hello there,

I was just going through the recurrence relationships for the negative binomial and poison distribution, and i have no idea how they came up with the recurrence formula. Please anybody that can help explain how this is done will be of great help. And will also help me understand more things in the future.

And please if you are currently preparing on taking the CS1 exam in April or September, please message me on +44(0)7404539272 either on WhatsApp or telegram.

Regards,
Ashih.
 
These formulae are just describing how P(X=x) can be calculated if we already know P(X=x-1). Eg, if X~Poi(m), then:

P(X=x) = e^(-m) m^x /x!

and

P(X=x-1) = e^(-m) m^(x-1) /(x-1)!

So

P(X=x) = e^(-m) m^(x-1) m / [x(x-1)!] = P(X=x-1) * m/x

You don't have to use recursive formulae to calculate probabilities though. Just use whichever method you find quickest.
 
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