Find the median and the mode for the Rayleigh distribution

(see Question 31 in Exercises 13.4.5). Also show that the mean is given by

which can be shown to be √(1/2πa). Compare these quantities when a = 6, and find the interquartile range.

Data from Question 31

The wave amplitude X on the sea surface often has the following (Rayleigh) distribution:

where a is a positive constant. Find the distribution function and hence the probability that a wave amplitude will exceed 5.5 m when a = 6.

Transcribed Image Text:

fx (x) = a exp(-22) 2a 0 (x > 0) (otherwise)