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If X Has a Poisson Distribution with Variance 2, Find - Mathematics and Statistics

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प्रश्न

If X has a Poisson distribution with variance 2, find P(X ≤ 4) 

[Use e-2 = 0.1353] 

योग

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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2015-2016 (July)

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