Sufficient statistic based on a random sample of size n where the pmf is P_theta(X=x)=c(theta)2^(−x/theta)

Maribel Mcintyre

Maribel Mcintyre

Answered question

2022-10-28

Sufficient statistic based on a random sample of size n where the pmf is P θ ( X = x ) = c ( θ ) 2 x / θ

Answer & Explanation

Annabella Ferguson

Annabella Ferguson

Beginner2022-10-29Added 15 answers

By definition, if a statistic is sufficient, the likelihood of the data depends on the data only through the statistic. By contrast, different data can lead to different i X i (and thus a different likelihood) but the same X ( 1 ) , and vice versa. Thus neither of these components is sufficient by itself.

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