Question

The occurrence of hurricanes in a coastal region may be modeled by a Poisson process. If the mean occurrence rate of hurricanes is once in every 10 months, determine the probability of
a) no hurricanes in 2 years,
b) at least three hurricanes in 2 years.

The maximum wind speed of hurricanes usually shows considerable fluctuations. Suppose that those recorded in this region can be fitted satisfactorily to a normal distribution with mean 34 m/s and standard deviation 6 m/s. If a structure in this region is designed for a wind speed of 45 m/s;
What is the probability that the structure wil

Answer 1

c) What is the probability that the structure will be damaged (i.e. design wind speed will be exceeded) by the next hurricane?
d) What is the probability that the structure will not be damaged in the next 5 years? (Assume statistical independence between damages).

Answer 2

on every ten months, there are 24 months in 2 years, so you expect how many in two years?

Answer 3

i guess it would be 2.4 so put \(\lambda=2.4\) and for the first one
\[P(x=0)=e^{-\lambda}=e^{-2.4}\] and then a calculator

Answer 4

at least 3 means not none, not one and not two so you compute
\[P(X=0)=e^{-2.4}\]
\[P(X=1)=2.4e^{-2.4}\]
\[P(X=2)=\frac{2.4^2e^{-2.4}}{2}\] add them up and subtract the total from one