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Since  is computed from a random sample, each sample may (usually, will) lead to different values for  and we may never get a value for  that is exactly equal to q, i.e, = q + "estimation error"

is also a random variable with its own sampling distribution (based on repeated sampling) and has its own mean, say and S.D., say .

Fact: There may be several different point estimators that may be considered "reasonable" for a parameter. The objective of estimation is not just to find an estimator and the corresponding estimate, but also to choose a good estimator. A good estimator is defined as one that is

• UNBIASED: E() = q , i.e., E["estimation error"] = 0,
• has MINIMUM VARIANCE: Var() must be minimized, i.e., be smaller than the variance of any other reasonable estimator.

• = (sample mean),
• =s² (sample variance),
• binomial parameter  (sample fraction defective),
• Poisson (or Exponential) parameter 

The standard error of an estimator is its S.D., = and it is usually estimated by .

For example,

• If =, then
• = if s is known, otherwise it is estimated via =.
• If  then
• if p and q are known,
• otherwise it is estimated as 

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