The yearly levels of water in the river Camse are independent random variables , with a given continuous distribution function and . The levels have been observed in years and their values recorded. The local council has decided to construct a dam of height
Let be the subsequent time that elapses before the dam overflows:
(a) Find the distribution function , and show that the mean value
(b) Express the conditional probability , where and , in terms of .
(c) Show that the unconditional probability
(d) Determine the mean value .