Suppose that a certain large population contains k different types of individuals (k 2), and let i denote the proportion of individuals of type i, for i 1, , k Here, 0 i 1 and 1 k 1 Suppose also that in a random sample of n individuals from this population, exactly ni individuals are of type i, where n1 nk n Find the M L E s of 1, , k

Question: Suppose that a certain large population contains k different types of individuals (k 2), and let i denote the proportion of individuals of type

Suppose that a certain large population contains k different types of individuals (k ≥ 2), and let θi denote the proportion of individuals of type i, for i = 1, . . . , k. Here, 0 ≤ θi ≤ 1 and θ1 + . . . + θk = 1. Suppose also that in a random sample of n individuals from this population, exactly ni individuals are of type i, where n1 + . . . + nk = n. Find the M.L.E.’s of θ1, . . . , θk.

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