extreme wave load follow Poisson distribution with an an occ

extreme wave load follow Poisson distribution with an an occurence rate lamda=0.01 per year. what is the probability of occurence of two extreme loads in a year? what is the probability of occurence of no extreme loads in a 2 years? what is the probability of one or two load occurence during a period of 25 years?

Solution

Possion Distribution
PMF of P.D is = f ( k ) = e- x / x!
Where   
= parameter of the distribution.
x = is the number of independent trials
  
Per one year an occurence rate lamda=0.01
For 2 Year the occurence rate = 2*0.01 = 0.02

a)
P( X = 2 ) = e ^-0.02 * 0.02^2 / 2! = 0.0002
b)
P( X = 0 ) = e ^-0.02 * 0.02^0 / 0! = 0.9802
c)
For 25 Year the occurence rate = 25*0.01 = 0.25
P( X = 1 ) = e ^-0.25 * 0.25^1 / 1! = 0.1947
P( X = 2 ) = e ^-0.25 * 0.25^2 / 2! = 0.0243

P( X = 1 or 2) = 0.1947+0.0243=0.219