Homework Assignments
Homework 2

Suppose
is a r.v. with c.d.f.
. Prove the following:
 is nondecreasing.
 .
 .
 is right continuous.
 if .

Show that the following are valid p.m.f.s:
 Binomial: if .
 Poisson: for .
 Find the mean and variance of when is (a) ; (b) Binomial ; (c) Poisson ; (d) Exponential . Do not use characteristic functions.

Suppose that
and
are jointly continuous. Show that
 Suppose that and are jointly Gaussian with parameters . Show that .
 Suppose , and define . Are and uncorrelelated? Are and independent? Find the p.d.f. of . Are and jointly continuous?
 Show that .
 Suppose . Use the ch.f. of to find an expression for , .
Problems from the Grimmett & Stirzaker text:
 Ex 1.4.4
 Ex 1.4.5. Hint: Let be the event that the th door conceals the car, let be the event that you see a goat, and let be the event that you see Bill.
 Ex 1.5.1.
 Ex 1.5.2
 Ex 1.5.7.
 Prob. 1.8.5
 Prob. 1.8.6.
 Prob. 1.8.19.
 Prob. 1.8.20.
 Prob. 1.8.30.
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/hw2.html.
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