The reliability of a dam is defined as the total water level (above seabed), H, should not exceed the total height of the dam (50 m). The maximum water level, H, depends on sum of mean sea level, Y, and the wave height, X, above the mean sea level. In a given storm condition, the dam may be overtopped depending on the wave height X. Equations below represents the Probability Density Function of annual mean sea level Y and extreme wave height, X. Determine: a. The probability of the water level overtopping the dam during an extreme storm condition. 5% b. If the dam was overtopped during the storm, what is the probability that the wave height is exceeding 30 m (X 30 m)? 5% c. If the desired reliability is 99.999% (i.e. 99.999% time the water level do not overtops the dam) over the dam life time 20 years, what should be the minimum height of the dam? 1 f(y)= 25 my 35 m b-a f(x)= 0.1-0.00667x+1.1x10x 0 x 40 m 5%