The number of complaints which a bank manager receives per day follows a Poisson distribution with parameter m = 4. Find the probability that the manager receives only two complaints on a given day - Mathematics and Statistics

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Sum

The number of complaints which a bank manager receives per day follows a Poisson distribution with parameter m = 4. Find the probability that the manager receives only two complaints on a given day

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Solution

Let X denote the number of complaints which a bank manager receives per day.
Given, m = 4 and e–4 = 0.0183

∴ X ∼ P(m) = X ∼ p(4)

The p.m.f. of X is given by

P(X = x) = `("e"^-"m" "m"^x)/(x!)`

∴ P(X = x) `("e"^-4(4)^x)/(x!), x` = 0, 1, 2,...

P(only two complaints on a given day)

= P(X = 2)

= `("e"^-4 (4)^2)/(2!)`

= `(0.0183 xx 16)/(2)`

= 0.1464

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