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Let X1,X2,...,Xn be i.i.d. Geometric(θ), θ = 1,2,3,... random variables. a) Find the maximum likelihood estimator...

Let X1,X2,...,Xn be i.i.d. Geometric(θ), θ = 1,2,3,... random variables.
a) Find the maximum likelihood estimator of θ.


b) In a certain hard video game, a player is confronted with a series of AI opponents and has an θ probability of defeating each one. Success with any opponent is independent of previous encounters. Until first win, the player continues to AI contest opponents. Let X denote the number of opponents contested until the player’s first win. Suppose that data of 10 players was collected: 7,4,3,1,12,10,2,1,4,6
What is the MLE of the probability that a player contests five or more AI opponents in a game until the first win?

Math   Statistics-And-Probability   
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