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STAT 801
Problems: Assignment 3
Suppose
are iid real random variables with
density f . Let
be the X 's arranged
in increasing order.
- Find the joint density of
.
- Suppose
. Prove that
is independent of
.
- Find the density of
.
- Find the density of
.
Suppose
are iid exponential. Let
.
- Find the joint density of
.
- Find the joint density of
.
Suppose
are iid N(
,
).
Let
. Let
.
- Develop a recurrence relation for
and
, expressing
and
in terms of
and
.
- Find the joint density of
.
- Generate data from N(0,1). By adding
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
.
- Show that
and
are independent.
- Show that
is uniformly
distributed on
.
- Show
is a Cauchy random variable.
Richard Lockhart
Thu Oct 10 22:15:37 PDT 1996