Problems: Assignment 3
Suppose 
are iid real random variables with
density f . Let 
be the X 's arranged
in increasing order.
.
. Prove that 
is independent of 
.
.
.
Suppose 
are iid exponential. Let 
.
.
.
Suppose 
are iid N(
,
).
Let 
. Let 
.
and 
, expressing
and 
in terms of 
and 
.
.
to the data for
some large values of k compare the numerical performance of these
recurrence relations to that of the one pass formula using
, 
and the usual computing formulas
for the sample variance.
Suppose X and Y are iid 
.
and 
are independent.
is uniformly
distributed on 
.
is a Cauchy random variable.