1. List Kolmogorovs axioms.
2. What is an event? Give me the general denition, not an example.
3. Suppose we select k objects out of n objects. How many ways can we do this in the following cases?
a.
Stat 322 (Spring 2016): Homework 2
due date is Friday, Jan 29th, in class
Note on problem #3.
3. A hacker wants to break into a computer, which is password-protected. Assume that there are 300 equally
Stat 322 (Spring 2016): Homework 6
due date is Friday, Mar 4th, in class
Show all of your work, and please staple your assignment if you use more than one sheet. Write your name
and the course number
Stat 322 (Spring 2016): Homework 3 Solutions
Show all of your work, and please staple your assignment if you use more than one sheet. Write your name
and the course number on every sheet.
1. Let X be
Stat 322 (Spring 2016): Homework 5 Solutions
Show all of your work, and please staple your assignment if you use more than one sheet. Write your name
and the course number on every sheet.
1. The time,
EE/STAT 322: Probabilistic Methods for Electrical Engineers
Midterm Exam 3 April 15, 2013
Student:
You have 50 minutes to finish the problems. The number points for each problem is provided. The
perfe
STAT 322 Homework 6, due in class WEDNESDAY, FEB. 29
1. Suppose that nominal 20 lb. bags of sand are produced in such a way that the actual weights
are normally distributed with a mean of 20.50 lb. an
STAT 322 Homework 7, due in class March 9
Suppose X is a continuous random variable with the following pdf:
(
fX (x) =
0, x < 0, x > 2
x/2, x [0, 2]
1. What are E(X) and V ar(X)?
2. Suppose X1 , X2 ,
STAT 322 Homework 8, due in class March 23
1. Suppose W (t), t cfw_0, 1, 2, 3, 4, ., is a Bernoulli process with p = 0.25. W is split into two
processes, X1 (t) and X2 (t) with probability 0.5 each. I
STAT 322 Homework 9, due in class April 13
1. A controlled experiment was conducted to examine the effect of temperature on the resistance
of wire made of two different alloys. Under the same conditio
STAT 322 Homework 5, due in class Feb. 24
1. Suppose the random variable X has the probability density function (pdf):
(
fX (x) =
3(1 x)2 0 x 1
0
x = other
(a) Prove that this is or isnt a legal pdf.
Solutions of Quiz 2
Problem1:
P(the system is operational)=1-P(the system is not operational)
Since the failures of the generators are mutually independent, we have
P(the system is not operational)=P(
EE/STAT 322: Probabilistic Methods for Electrical Engineers
Midterm Exam 2 Mar. 06, 2013
Student:
You have 50 minutes to finish the problems. The number points for each problem is provided.
The perfec
EE 322 Final Exam, Spring 2011
May 4, 2011
STUDENT NAME:
Total Time: 2 hours
4 problems, plus a 5th bonus problems
I need to see JUSTIFICATIONS FOR EACH STEP if you want to get credit for your solutio
2. (20 points)
Spam emails can be quite effectively identified by Bayesian filters. Suppose that 20% of all
emails are spam emails. Among all spam emails, 10% contain a dollar sign ($) in the subject
Stat 322 - Homework 2
Maximum score: 20 points; due Thursday, September 10, 2015
1
System Reliability
Find the probability that the following ve-component system works (that is, there is an
unbroken p
STAT 322 Homework 1, due in class Jan. 20
1. A nuclear power plant of a particular design contains 6 back-up water pumps used to cool
the core if the primary components fail. Suppose the events of int
STAT 322 Homework 3, due in class Feb. 3
1. A random variable is generated in the following way. First, a fair die is tossed, and the
resulting number (1-6) is observed. Then a fair coin is tossed tha
STAT 322 Homework 2, due in class Jan. 27
1. A certain company has had trouble with shipments of equipment that are damaged during
transport from the facility at which they are manufactured (A) to the
STAT 322 Homework 4, due in class Feb. 10
A small computer lab contains four fairly unreliable workstations. On any given evening, the probability that any workstation is operating is 0.7, and the ope
Stat 322 (Spring 2016): Homework 1 Solutions
Show all of your work, and please staple your assignment if you use more than one sheet. Write your name
and the course number on every sheet.
1. Sample sp