The average of the greatest snow depths for each winter at a location of interest is 80 cm, and the standard deviation (reflecting year-to-year differences in maximum snow depth) is 45 cm. a. Fit a...

The average of the greatest snow depths for each winter at a location of interest is 80 cm, and the standard deviation (reflecting year-to-year differences in maximum snow depth) is 45 cm.

a. Fit a Gumbel distribution to represent this data, using the method of moments.

b. Derive the quantile function for the Gumbel distribution, and use it to estimate the snow depth that will be exceeded in only one year out of 100, on average.