Question

A machine releases a candy-bar with unknown probability q at a press of a button (each press is independent on others). Clearly, the number of attempts required to receive one bar is distributed according to Geo(q). Your sweet-tooth instructor wants n candy bars, which would take him an overall of

Sn := X1 + X2 + . . . + Xn

attempts. Here X1, . . . , Xn ∼ Geo(q) are independent.

A) Find the moment estimator of q given the (integer) observations X1, . . . , Xn > 0.

B) Write the likelihood function L(q) given the (integer) observations X1, . . . , Xn > 0.

C) Find the maximum likelihood estimator of q (by either likelihood or log-likelihood).

Answer 1

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