This problem presents an algorithm for drawing a simple

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QUESTION:

This problem presents an algorithm for drawing a simple random sample from a population in a sequential manner. The members of the population are considered for inclusion in the sample one at a time in some prespecified order (for example, the order in which they are listed). The ith member of the population is included in the sample with probability

\(\frac{n-n_{i}}{N-i+1}\)

where ni is the number of population members already in the sample before the ith member is examined. Show that the sample selected in this way is in fact a simple random sample; that is, show that every possible sample occurs with probability

\(\frac{1}{\left(\begin{array}{l}N \\ n\end{array}\right)}\)

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QUESTION:

This problem presents an algorithm for drawing a simple random sample from a population in a sequential manner. The members of the population are considered for inclusion in the sample one at a time in some prespecified order (for example, the order in which they are listed). The ith member of the population is included in the sample with probability

\(\frac{n-n_{i}}{N-i+1}\)

where ni is the number of population members already in the sample before the ith member is examined. Show that the sample selected in this way is in fact a simple random sample; that is, show that every possible sample occurs with probability

\(\frac{1}{\left(\begin{array}{l}N \\ n\end{array}\right)}\)

ANSWER:

Step 1 of 2

An algorithm for drawing a simple random sample from a population in a sequential manner. The members of the population are considered for inclusion in the sample one at a time in some prespecified order (for example, the order in which they are listed).

The  member of the population is included in the sample with probability

where  is the number of population members already in the sample before themembers are examined.

It is required to show that the sample selected in this way is in fact a simple random sample; that is, every possible sample occurs with probability.

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