Question: Rainfall. Suppose that the distribution of annual rainfall in a particular place, measured in inches, is approximately gamma with shape parameter r = 3. If the mean annual rainfall is 20 inches, find approximations to the following:
a) The probability of more than 35 inches of rain in any particular year:
b) The probability that in ten consecutive years, it never rains more than 35 inches, assuming different years are independent:
c) Still assuming independence of different years, the probability that the record rainfall over the last 20 years is exceeded in at least one of the next ten years, assuming the record rainfall over the last 20 years, R20 say, is known:
d) Same as c), but assuming the value of R20 is unknown.