Question

A rogue wave is a unusual, unpredictable, large wave that dwarfs those around it. The impact of such a wave can threaten ocean-going vessels, and is thus of interest to various weather forecasting agencies. In the south Atlantic, the average for this rare event is estimated by the European Center for Medium-Range Weather Forecasts to be 0.0377 rogue waves per hour. If a ship just encountered a rogue wave, what is the probability (correct to 4 decimal places) that at least a day will pass before it comes across another rogue wave?

Show work please.

Answer 1

Probability of rogue wave per hour = 0.0377

n = 24

mean = = n * p = 24 * 0.0377 = 0.9048

Let x be a random variable which is equal to number of waves in a day (24 hours); where X Po(0.9048)

Since the events are independent, wave occuring will not impact the probabiltiy of second event. (zero wave atleast a day)

Hence we need to find the probabiltiy that there will be no wave in 24 hours. i.e. X= 0

ANS: Probability that atleast a day will pass before it comes across another rouge wave = 0.4046