The Range as a Median Interval
Six independent observations are drawn from the same continuous distribution (otherwise unknown). The interval [smallest, largest] is used as a confidence interval for the population median. What is its exact coverage probability, that is, the probability that the median lies between the smallest and largest of the six observations? Give a reduced fraction.
Related problems
Source: Classic distribution-free confidence interval for the median via order statistics; folklore in nonparametric statistics. Statement written for AxiomIQ.