# Estimation of discrete random variable

Suppose you have a discrete random variable $X_1$ with known probability mass function. I guess that choosing a variable drawn from the same pmf would be the best way to guess $X_1$ assuming all experiments are independent. If this is true, what is the name of this theorem?

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"Best" in what sense? –  cardinal Nov 21 '11 at 23:44
the one that minimizes the probability of error (it's a repeated experiment) –  ACAC Nov 21 '11 at 23:49
If you want to minimize the probability of error, then you'd just always select as an estimator any mode of the distribution. –  cardinal Nov 21 '11 at 23:50
if you have a discrete r.v. with two values and probabilities $p_1$ and $1-p_1$ the mode does not minimize the probability of error. If you draw a r.v. from the same pmf the probability of error decreases. –  ACAC Nov 22 '11 at 0:00
Either I'm not understanding your question quite right or you need to double-check your claim. –  cardinal Nov 22 '11 at 0:09