Past exam of the mathematics course of the University of Cambridge / 2024 / ib / Paper 1 / 6H / d / Solution

The joint density depends on the sample through

\sum_{i = 1}^{n} X_{i}^{2},

not merely through

\sum_{i} ∣ X_{i} ∣

. For example, after padding with zeros when

n > 2

, take

x = (1, 1, 0, \dots, 0), y = (2, 0, 0, \dots, 0) .

Both samples have sum of absolute values

2

, but

\frac{p _{σ} ( x )}{p _{σ} ( y )} = exp (\frac{1}{σ ^{2}}),

which depends on

σ

. The likelihood-ratio necessary condition for sufficiency fails, so

i = 1 \sum n ∣ X_{i} ∣ is not sufficient .

 Ancestors (11)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version