QUESTION a

Bombardment of a certain atomic nucleus can result in 5 types of disintegrations. On examining photographic records of such disintegrations, X are found to be of the first type.

1. Show that X/n is an unbiased estimator of the probability of a disintegration being "first type".

2. Explain why unbiasedness is usually thought to be a desirable property.

QUESTION b

Symmetry considerations imply that the probability of the second type of disintegration is also variance. If Z is the number of the disintegrations which are either first or second type,

1 find an unbiased estimator of variance based on Z.

2 is it preferable to the one based on X? ( give reasons)