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प्रश्न
If X has a Poisson distribution with variance 2, find P(X ≤ 4)
[Use e-2 = 0.1353]
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उत्तर
P(X ≤ 4) = P (X = 0) + P(X =1) + P (X = 2) + P(X = 3) + P(X = 4)
`= ("e"^-2 2^0)/ (0!) + ("e"^-2 2^1)/ (1!) + ("e"^-2 2^2)/ (2!) + ("e"^-2 2^3)/ (3!) + ("e"^-2 2^4)/ (4!)`
`= "e"^-2 (1 + 2 + 4/2 + 8/6 + 16/24)`
= 0.1353 × 7
= 0.9471
∴ P(X ≤ 4) = 0.9471
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