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 * 2.5²⁾ / 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 * 0.5¹⁾ / 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} * 8.0³⁾ / 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} * 3.7¹⁰⁾ / 10! = 0.0033

Probability = 0.0033