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प्रश्न
In a town, 10 accidents take place in the span of 50 days. Assuming that the number of accidents follows Poisson distribution, find the probability that there will be 3 or more accidents on a day.
(Given that e-0.2 = 0.8187)
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उत्तर
Here, m = 0.2 and X ∼ P(0.2) with parameter m.
The p.m.f. of X is X ∼ P(m).
P(X = x) = `(e^(−m) . m^x)/(x!), x = 0, 1, 2,...`
P(X ≥ 3) = 1 − P(X < 3)
= 1 − [P(0) + P(1) + P(2)]
= `1 − [(e^(− 0.2)(0.2)^0)/(0!) + (e^(−0.2)(0.2)^1)/(1!) + (e^(−0.2)(0.2)^2)/(2!)]`
= 1 − [0.8187(1 + 0.2 + 0.02)]
= 1 − 0.998814
= 0.001186
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