Discussion
A systematic sample of size 2 is drawn from a finite population with \(N = 4\) and \(k = 2\). The samples are drawn independently of each other. The probability that the two units (2, 4) are included in sample equals :
Answer: B
The probability is 1/2.
With \(N = 4\) and sampling interval \(k = 2\), a random start \(r \in \{1, 2\}\) is chosen with probability 1/2 each, and the sample is \(\{r, r + 2\}\). The only possible samples are {1, 3} and {2, 4}, each with probability 1/2.
So the units 2 and 4 appear together exactly when the start is 2, with probability 1/2. It is not 0, since {2, 4} is a possible sample, and not 1/4, which would treat the six pairs of a simple random sample as if they were possible here.
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