<P> J. Vitter in 1985 proposed reservoir sampling algorithm which is often widely used . This algorithm does not require advance knowledge of n and uses constant space . </P> <P> Random sampling can also be accelerated by sampling from the distribution of gaps between samples, and skipping over the gaps . </P> <P> Consider a school with 1000 students, and suppose that a researcher wants to select 100 of them for further study . All their names might be put in a bucket and then 100 names might be pulled out . Not only does each person have an equal chance of being selected, we can also easily calculate the probability (P) of a given person being chosen, since we know the sample size (n) and the population (N): </P> <P> 1 . In the case that any given person can only be selected once (i.e., after selection a person is removed from the selection pool): </P>

Simple random samples give an unbiased picture of the sampling frame