Help with poisson distribution

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16 Jan 2008
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The teacher managed not to cover this in enough detail and I'm stuck on this question:

Given a poisson distribution: X~Po(n)
If P(X=5) = P(X=4)+P(X=3), find the value of n.

Any help?

Cheers!
 
Doesn't matter anymore. Someone somewhere else who doesn't try and make a joke out of absolutely everything showed me how. And thanks Jay Psi.
 
I have a solution and I hope it is right, lol.

X~Poi(n)

Given that the PMF of the Poisson dist is P(X = k) = (e^-n * n^k)/k! we can form a polynomial:

(e^-n * n^5)/5! = (e^-n * n^4)/4! + (e^-n * n^3)/3!
Multiply by 5!/e^-n to get:
n^5 - 5n^4 - 20n^3 = 0
Factorise
n^3(n^2 -5n - 20) = 0
Use quadratic formula and u get solutions
n = 0 (thrice), 7.623475 and a negative value.

The poisson dist has the requirement that the parameter, n > 0, so I would take n = 7.623475 as the solution (assuming I didn't make any silly mistakes).
Yeh thats right.. Thanks for the help :D
 
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