2. Use the Lehman-Scheffe´ minimal sufficiency theorem, or some other argument, to find a set of minimal sufficient statistics for each case below.

a. You are random sampling from a log-normal population distribution given by fðz; m; s2Þ ¼ 1

ð Þ 2p 1=2 sz exp  1 2s2 ð Þ lnðzÞ  m 2

 Ið0;1Þ ðzÞ;

where m∈(1,1) and s2 > 0.

b. You are random sampling from a “power function”

population distribution given by f zð Þ¼ ; l lzl1 Ið0;1ÞðzÞ; where l>0: