Question

6.33 During the dry month of August, one U.S. city has measurable rain on average only two days per month. If the arrival of rainy days is Poisson distributed in this city during the month of August, what is the average number of days that will pass between measurable rain? What is the standard deviation? What is the probability during this month that there will be a period of less than two days between rain?

Answer 1

Let, X be the arrival of rainy days in one U.S. city during the month of August and it is follows Poisson distribution with mean 2 days. So pdf is as

   , x= 0,1, ........

And here given that,

a) The average number of days that will pass between measurable rain is 2 because

b) And variance(X) =

So standard deviation (X) = 1.4142

e) P(During this month that there will be a period of less than two days between rain) = P(X<2) = p(X=0) + P(X=1)

= 0.1353 + 0.2707 = 0.406

i.e. probability during this month that there will be a period of less than two days between rain is 0.406.