Question: For Y i i i d Bernoulli ( p ) , consider ^ p = n i = 1 Y i n as an estimator

  1. For Y i i i d Bernoulli ( p ) , consider ^ p = n i = 1 Y i n as an estimator for p .

a. Find the Fisher information for I Y ( p ) .

b. Find V ( ^ p ) .

c. Is ^ p an efficient estimator for p ? Why or why not?

2 Let Y 1 , ... , Y n be a random sample with pdf

f ( y ) = y 1 , 0 0 .

Show that Y is a consistent estimator of / ( + 1 ) .

For Y i i i d Bernoulli ( p ) , consider

\f

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