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Question
If X has Poisson distribution with m = 1, then find P(X ≤ 1) given e−1 = 0.3678
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Solution
Given, m = 1 and e–1 = 0.3678
∴ X ~ P(m) = X ~ P(1)
The p.m.f. of X is given by
P(X = x) = `("e"^-"m" "m"^x)/(x!)`
∴ P(X = x) = `("e"^-1 1^x)/(x!), x` = 0, 1, 2,...
∴ P(X ≤ 1) = P(X = 0 or X = 1)
= P(X = 0) + P(X = 1)
= `("e"^-1 1^0)/(0!) + ("e"^-1 1^1)/(1!)`
= `(0.3678 xx 1)/(1) + (0.3678 xx 1)/(1)`
= 0.7356
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