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)
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
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