A nuclear facility in a coastal region is built to withstand ocean wave forces. Suppose the annual maximum wave height of the ocean waves (above the sea level) is a lognormal random variable with mean height of 4.0 meters and a c.o.v. of 0.8
a) What is the probability that the wave height will exceed 6 meters in a given year?
b) To construct the nuclear facility in a safe manner, an engineer is assigned to compute a design wave height (above sea level) that will not be exceeded by ocean waves over a 10 year period with a probability of 95%, i.e., P(non-exceedence over 10 years) = 0.95. Assuming that wave height exceedences between years are statistically independent, what should be the height of the design wave above the sea level?
c) Suppose that ocean waves exceeding 6 meters will occur according to a Poisson process and that each of these waves could potentially cause damage to the facility with a probability of 0.4. What is the probability that there will be no damage to the facility in 10 yr? Damages to the facility between waves are statistically