Question

The average number of rainfall events and storms in one month in an area is 10.
a. Calculate the chance that more than 1 rain event and a storm will strike the area in a 2 week period.
b. What is the average number of rainfall events and storms affecting the area in a period of 2 months

Answer 1

Let X = number of rainfall events and storms in one month in an area.

X follows Poisson distribution with parameter = 10

a.

Let Y = number of rainfall events and storms in an area in 2 weeks.

Since period is exactly half as in case of X, the parameter becomes = 10 / 2 = 5

Hence Y follows Poisson distribution with parameter = 5

The pmf of Poisson distribution is,

Now we find probability at point y = 0 and y=1 by using above pmf.

Similarly we obtain P(Y=1) = 0.0337

Hence

b.

Let Z = number of rainfall events and storms in an area in 2 months.

Since period is exactly double as in case of X, the parameter becomes  2= 2*10 = 20

Hence Z follows Poisson distribution with parameter = 20

We know that mean of Poisson distribution is .

Therefore the average number of rainfall events and storms affecting the area in a period of 2 months is 20.