Reconsider your assessed 0.05 and 0.95 fractiles in Problem 8.13.If you are perfectly calibrated when judging these fractiles, then you would expect that in any given situation the actual value has a 0.90 chance of falling between your assessed fractiles (for that variable).
a. Assuming you are perfectly calibrated, what is the probability that0, 1, or 2 of the 10 actual values fall between the assessed fractiles?
b. To justify using the binomial distribution to answer part a, you must assume that the chance of any particular value falling between its fractiles is the same regardless of what happens with the other variables. Do you think this is a reasonable assumption? Why or why not?