A lake contains 4 distinct types of fish. Suppose that each fish caught is equally likely to be any one of these types. Let denote the number of fish that need be caught to obtain at least one of each type.

a. Give an interval (a, b) such that P{a ≤ Y ≤ b} ≥ .90.

b. Using the one-sided Chebyshev inequality, how many fish need we plan on catching so as to be at least 90 percent certain of obtaining at least one of each type?