Algorithms run repeatedly on many inputs. System noise affects each run.

You summarize performance with one value.
An estimate of average run time.

This is point estimation in computer science.

Let X represent run time from one execution.

The population mean run time is μ.

The sample mean estimates μ.

\[ \mu = E(X) \]

\[ \hat{\mu} = \bar{X} = \frac{1}{n}\sum_{i=1}^{n} X_i \]

You measure run time in milliseconds.
You repeat the algorithm many times.

The sample mean estimates the true mean runtime.

## [1] 118.2637

Bias measures systematic error of an estimator.

\[ \text{Bias}(\hat{\mu}) = E(\hat{\mu}) - \mu \]

For the sample mean.

\[ E(\bar{X}) = \mu \]

Therefore, the sample mean is unbiased.

Larger samples give more stable estimates.

Point estimation gives one number for an unknown parameter.
In computer science, you use it for benchmarking run time.
The sample mean estimates the true mean run time.
Larger samples reduce variability in the estimate.