Question

If X has Poisson distribution with parameter m = 1, find P[X ≤ 1]. (Use e–1 = 0.3679)

Answer 1

We have, the Poisson distribution is given by  

p(r)=e-m.m^r/r! 

Here                m = 1 (given) 

Then `P(X ≤ 1) = p(0)+p(1)` 

= `(e^-m.(1)^0)/(0!)+(e^-1(1)^1)/(1!)` 

=`e^-1+e^-1` 

= `2e-1` 

=2(0.3679) 

`e^-1=0.3679` (given) 

= 0.7358