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Step-by-step answer to Poisson Distribution

Let X be a random variable which follows Poisson Distribution. Assume that the probability P(X=1)=P(X=2), find P(X=3).

Solution This solution is FREE courtesy of BrainMass!

Solution. Assume that P(X=k)=e^(-a)*a^k/k!,
k=0,1,2,..., a>0 is a constant.

Since P(X=1)=P(X=2)

e^(-a)* a/1!=e^(-a)*a^2/2!

So, a=2.
Thus,
P(X=3)=e^(-2)*2^3/3!
=4/3e^(-2)