# Question

Suppose we wish to estimate the probability, PA, of some event A as outlined .As motivated by the result, suppose we repeat our experiment for a random number of trials, N. In particular, we run the experiment until we observe the event A exactly m times and then form the estimate of PA according to

Here, the random variable represents the number of trials until the m th occurrence of A.

(a) Find E [ṔA]. Is this estimate unbiased?

(b) Would it be better to use ṔA = m / N as an estimate?

Here, the random variable represents the number of trials until the m th occurrence of A.

(a) Find E [ṔA]. Is this estimate unbiased?

(b) Would it be better to use ṔA = m / N as an estimate?

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