Suppose you have concluded that your prior distribution for a parameter of interest is well represented by a Gumbel distribution. Evaluate the parameters of this distribution if a. The interquartile...

Suppose you have concluded that your prior distribution for a parameter of interest is well represented by a Gumbel distribution. Evaluate the parameters of this distribution if

a. The interquartile range of your prior distribution is (100, 400).

b. The mean and standard deviation of your prior distribution are 270 and 200, respectively.

c. What do these two distributions imply about your beliefs about the magnitude of the 100-year event?