Question

Over the past 15 years, the numbers of hurricanes per year to cause damage in a particular city were 4, 2, 1, 3, 0, 2, 1, 3, 5, 2, 3, 1, 1, 2, and 0.

What is the probability of not having hurricane damage in any 1 year?

What are the average and variance of the number of hurricanes in 1 year?

Answer 1

this can be approximated as poisson distribution with paramter =expected hurrican per year

=(4+2+1+3+0+2+1+3+5+2+3+1+1+2+0)/15=2

hence probability of not having hurricane damage in any 1 year =P(X=0)=e^-2*2⁰/0! =0.1353

average  number of hurricanes in 1 year ==2

variacne of hurricanes in 1 year ==2