The aggregate annual rainfall at a given location is modeled as a random variable, resulting in a sequence of random variables {
V1, V2, V3, ...} for years 1, 2, 3,.... Assume the V's are independent, lognormally-distributed random variables with a mean value of 32in, and a coefficient of variation of 50%. It is desirable for the annual rainfall to be in the range between 15in and 50in. If this fails to be the case for multiple years, this can have adverse environmental and economic consequences.A) Find the probability a = P(15in < Vi \leq 50in). B) For an arbitrary ten-year interval, nd the probability that the rainfall will not be in the desired range for at least three of the years in the interval.
