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Just a note

For example, if the statistic of interest is the sample mean, , its expected value, E[], is the population mean μY which is also the expected value of Y, E[Y]. Therefore, in that sense, the value of any randomly-selected observation can be considered to be an estimate of their expected value, their population's mean.

More generally the expected value of any estimator is the sum of each possible value of that estimate, i times the probability of obtaining it, pi, so E[] = Σ[pii].

However, in the case of smooth (known) functions of continuous variables, for reasons of mathematical convenience, you will find that statisticians prefer to express this summation using integral calculus.