Part CCSIR NET December 2024injective-functions-inherit-sufficiency

Injective functions inherit sufficiency

Let X, Y, Z be independent and identically distributed (i.i.d.) random variables, each following Bernoulli $(θ), 0 < θ < 1$ . Then, which of the following statements are true?

A. $(79 X + 2024 Y, 23 Z^{2})$ is a sufficient statistic for $θ$ .✓
B. $13 (X + Y + Z)^{3}$ is a minimal sufficient statistic for $θ$ .✓
C.2(X + Y + Z) is a complete sufficient statistic for $θ$ .✓
D.(X − 2Y + Z) is an ancillary statistic.

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.

See pricing

50 are analysed free — try those first.

Related counterexample: A sufficient statistic is complete

Injective functions inherit sufficiency

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