Homework Assignments
Homework 7
 Suppose is a homogeneous Poisson process with parameter . Define a random variable as the time of the first occurrence of an event. Find the p.d.f. and the mean of .
 Suppose { is a w.s.s. random process with autocorrelation function . Show that if is continuous at then it is continuous for all . (Hint: Use the Schwartz inequality.)

Under the conditions of problem 2, show that for
,

Suppose
and
are random variables with
and
. Define the random processes
and
by

Let
, where
is a homoegenous Poisson
counting process with rate
. Show that the differential
equation

Let
, where
is an inhomoegenous
Poisson counting process with timevarying rate
, where
is a continuous nonnegative function. Show that the
differential equation

Suppose
is a random process with power
spectral density

Suppose that
is a random variable with p.d.f.
and
is a random variable independent of
uniformly distributed in
. Define a random process by
 Suppose that is a w.s.s., zeromean, Gaussian random process with autocorrelation function and power spectral density . Define the random process by . Find the mean, autocorrelation, and power spectral density of .

Suppose
and
are independent random variables with
and
. Define random processes by
Copyright 2008,
Todd Moon.
Cite/attribute Resource
.
admin. (2006, June 13). Homework Assignments. Retrieved January 07, 2011, from Free Online Course Materials — USU OpenCourseWare Web site: http://ocw.usu.edu/Electrical_and_Computer_Engineering/Stochastic_Processes/hw7.html.
This work is licensed under a
Creative Commons License