Question

Assume a Poisson distribution. A) If ? = 2.5 , find P(X =2 ). B) If ? = 0.5find P(X =1) C) If ? = 8.0find P(X=3) D) If ? = 3.7find P(X =10)

Answer #1

Solution :

A ) Given that ,

= 2.5

x = 2

Using poisson probability formula,

P(X = x) = (e^{-}
*
^{x} ) / x!

P(X = 2 ) = (e^{-2.5} * 2.5^{2)} / 2! =
0.2565

Probability = 0.2565

B ) Given that ,

= 0.5

x = 1

Using poisson probability formula,

P(X = x) = (e^{-}
*
^{x} ) / x!

P(X = 1 ) = (e^{-0.5} * 0.5^{1)} / 1! =
0.3033

Probability = 0.3033

C ) Given that ,

= 8.0

x = 3

Using poisson probability formula,

P(X = x) = (e^{-}
*
^{x} ) / x!

P(X = 3 ) = (e^{- 8.0} * 8.0^{3)} / 3! =
0.0286

Probability = 0.0286

D ) Given that ,

= 3.7

x = 10

Using poisson probability formula,

P(X = x) = (e^{-}
*
^{x} ) / x!

P(X = 10 ) = (e^{- 3..7} * 3.7^{10)} / 10! =
0.0033

Probability = 0.0033

poisson process
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