## WHAT IS AN ESTIMATOR?

In Chapter 1 we stated that statistics is the science of estimating the probability distribution of a random variable on the basis of repeated observations drawn from the same random variable. If we denote the random variable in question by X, the n repeated observations in mathematical terms mean a sequence of n mutually independent random variables X, X2, . . . , Xn, each of which has the same distribution as X. (We say that (X;) are i. i.d.)

For example, suppose we want to estimate the probability (p) of heads

for a given coin. We can define X = 1 if a head appears and = 0 if a tail appears. Then Xt represents the outcome of the zth toss of the same coin. If X is the height of a male Stanford student, X* is the height of the ith student randomly chosen.

We call the basic random var...

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