Homework Solutions
Utah State University
ECE 6010
Stochastic Processes
Homework # 5 Solutions

Let
and
(independent). Let
and
. Show that
and
Here we have,
Jacobian is given by
Now,
and

If
and
are independent and
,
show that
has density
.
Here and are independent and , therefore we have,

Let
and
. Let
. Show that

If
and
, show
that
is exponentially distributed.
We have,

Let
be a monotone increasing function and let
. Show that
Suppose that . Then

Let
. Show that
Solution: Introduce the auxiliary variable . Then

Let
and
be independent with
and
. Determine the density of:

.

.

.

Show that if
are i.i.d.
, then
has a Cauchy distribution,
We have