Question: A certain butterfly species is split into three types 1, 2 and 3, which occur in the genotypical proportions p1.#/ D #2, p2.#/ D 2#.1#/

A certain butterfly species is split into three types 1, 2 and 3, which occur in the genotypical proportions p1.#/ D #2, p2.#/ D 2#.1#/ and p3.#/ D .1#/2, 0 # 1.

Among n butterflies of this species you have caught, you find ni specimens of type i . Determine a maximum likelihood estimator T of #. (Do not forget to consider the extreme cases n1 D n and n3 D n.)

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