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Part BCSIR NET June 2024linearity-over-indicators

Linearity over indicators

The expected number of distinct units in a simple random sample of 3 units drawn with replacement from a population of 100 units is

  1. A.3−(99/100)33 - (99/100)^{3}
  2. B.100−993/1002100 - 99^{3}/100^{2}✓ Correct
  3. C.2+992/10032 + 99^{2}/100^{3}
  4. D.3−(99/100)23 - (99/100)^{2}

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward, and why this one tests execution slip.

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50 are analysed free — try those first.

The trap it tests

Execution slip

The idea was right. The computation was not.

Drill statements like this

Related counterexample: Systematic sampling is always at least as efficient as SRS

More on this topic

The chapter behind this: Sampling designs — free to read

From Sampling and Design of Experiments › SRS, stratified and systematic sampling

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