A rogue wave is a unusual, unpredictable, large wave that dwarfs those around it

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?

Explanation / Answer

A ship just encountered a rogue wave,

We want to find the probability that at least a day will pass before it comes across another rogue wave.

that is in the 24 hours at least one such wave pass the ship.

For this we can used Poisson distribution with patameter = 24*0.0377 = 0.9048

If X is a random variable takes values as number of rough wave pass in the 24 hours.

Then mathematically we need to find P( X >=1 )

P(X >= 1) = 1 - P(X = 0) = "=1-POISSON(0,0.9048,0)"

(excel command with x = 0, mean = 0.9048, and cumulative =0)

So we get P(X >= 1) = 0.5954 (this is the final answer).

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