Homework Assignments
Homework 5

Box Muller: Let
and
(independent). Let

If
and
are independent and
, show that
has the density

Let
and
be
independent. Let
. Show that
 If and , show that is exponentially distributed.

Let
be a monotone increasing function and let
. Show that

Let
. Show that

Let
and
be independent with
 .

Show that if
are i.i.d.
, then
has a Cauchy distribution,
 Exercise 4.4.3.
 Exercise 4.7.3.
 Exercise 4.7.4.
 Exercise 4.8.1 (Hint: Laplace transform)
 Exercise 4.8.2 (Hint: Laplace transform)
Copyright 2008,
Todd Moon.
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.
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