You want to design a mini-dam that collects water in the winter and you want to estimate what is the probability that it will overflow? If you know that the annual precipitation in the area has an average of 350 mm, a standard deviation of 240 mm and distributes Gamma of two parameters.

a) What would be the maximum magnitude of precipitation if you want to design it for a 10-year period? return? And if you designed it for a 20-year return period, what would be the precipitation maximum?

b) If you design it for a 20-year payback period, you have the budget to fix the mini dam 1 time, how likely is it that it will fail 2 times in the next 20 years and run out of dam?

c) If you design it for a 10-year payback period, you have the budget to fix the mini dam 2 times, how likely is it that it will fail 3 times in the next 20 years and run out of dam? Which design would you go with?