Homework 5  Due Feb 28


Suppose X1, X2, ... Xn  is iid exp( lambda ) distribution.

Show that  \bar X  -->  1/lambda  in probability as n -> infinity.

show  \sqrt {n} [ 1/ \bar X - lambda ]  --> normal distribution, also identify the parameters of 
the limiting normal distribution

Can you find (and proof)  \sqrt n [ 1/ \barX  - lambda]/ ?  --> N(0,1)
(so that ? should be computable from sample, not involve parameter lambda).



Problems from our textbook

6.1

6.2

6.3

6.7


If X1 is Poisson( lambda)
   X2  is Poisson( 3*lambda) and X1 indep X2.
Find a one-dim sufficient statistics for lambda.