- #1
mliuzzolino
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Homework Statement
A random variable has a Poisson distribution with parameter λ = 2. Compute the following probabilities, giving an exact answer and a decimal approximation.
P(X ≥ 4)
Homework Equations
P(X = k) = λke-λ/k!
The Attempt at a Solution
P(X ≥ 4) = Ʃk = 4∞ λke-λ/k!
= λ4e-λ/4! + λ5e-λ/5! + λ6e-λ/6! + [itex]\cdots[/itex]
= e-λ [λ4/4! + λ5/5! + λ6/6! + [itex]\cdots[/itex]]
= e-λ Ʃk = 4∞ λk/k!
Let n = k - 4
=e-λ Ʃn = 0∞ λn+4/(n+4)!
plug in λ = 2
= e-2 Ʃn = 0∞ 2n+4/(n+4)!
= e-2 Ʃn = 0∞ 2n24/(n+4)!
= 16e-2 Ʃn = 0∞ 2n/(n+4)!
This is as far as I have gotten, but I'm not sure I'm on the correct track. I used wolfram alpha to reduce the summation term, Ʃn = 0∞ 2n/(n+4)!, to [1/48(3e2-19)], but I'm at a loss as to how to get there myself.
Anyone have any suggestions? It would be greatly appreciated!