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We have a Poisson distribution with mean = 4. Find P(X = 3), P(X < 3), P(X <= 3), P(X > 3), the variance, and standard deviation

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Answer

The probability mass function is

$graphic$

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So,

P(X = 3) = [e^(-4)*4^3]/3! = 0.195367

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.018316 + 0.073263 + 0.146525 = 0.238104

P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.238104 + 0.195367 = 0.433471

P(X > 3) = 1 - P(X ≤ 3) = 1 - 0.433471 = 0.566529

-----

Mean = λ = 4

Standard deviation = √λ = √4 = 2

Sincerely,
Sk1llz

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Expert:	Sk1llz
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Answered:	2/21/2009

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We have a Poisson distribution with mean = 4. Find P(X = 3), P(X < 3), P(X <= 3), P(X > 3), the variance, and standard deviation

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