## MAXIMUM LIKELIHOOD ESTIMATOR: DEFINITION AND COMPUTATION

Suppose we want to estimate the probability (p) that a head will appear for a particular coin; we toss it ten times and a head appears nine times. Call this event A. Then we suspect that the coin is loaded in favor of heads: in other words, we conclude that p = У2 is not likely. If p were У2, event A would be expected to occur only once in a hundred times, since we have P(A I p = У2) = CI°(V,)10 = 0.01. In the same situation p = % is more likely, because P(A p = 3/4) = С9°(3/4)9(У4) s= 0.19, and p = 9/10 is even more likely, because P(A p = 9/ю) = С9°(9/ю)9(Уіо) — 0.39. Thus it makes sense to call P(A p) = СІ°р9(1 — p) the likelihood function of p given event A...

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