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. Unordered, with replacement.
b. Unordered, without repl
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 on every sheet.
1. Suppose that the lifetimes of batter
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, in minutes, it takes to reboot a certain system is a c
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
perfect score is 100. You are only required to write necessa
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. and standard deviation of 0.75 lb. Assume
that the weight
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 , X3 , . ,X12 are independent, and each has the distribut
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. In turn, X1 is further split into two
processes, Y1 (t)
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 conditions:
25 wires of alloy A were tested, resulting in meas
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 space and Event. Suggest suitable sample space, , and ide
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. (In the following problem parts, assume that it
is.)
(b
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(failure of generator 1) P(failure of generator 2) . . .
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 perfect score is 100. You are only required to write necessar
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 solution,
please do not just provide final answers. You will n
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 line.
Among the non-spam emails, only 1% contain a doll
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 path from A to B). The number on top of each component g
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 interest to be:
E1 : all 6 pumps activate as designed
E2
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 that has a 1 on one side, and
a 2 on the other. The random
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 facility at which they
are used (B). On the other hand
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 operation (or lack of it) of any workstation
is independen
Stat 322 (Spring 2016): Homework 1
due date is Friday, Jan 22nd, 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 on every sheet.
1. Suggest suitable sample space, , an
Stat 322 (Spring 2016): Homework 2 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. A machine produces defective parts with three different probabil
Statistics 322
Spring 2016
Practice problems for Exam 2
Solutions
1. A continuous random variable X has the following probability density function (pdf):
1
x, for 0 < x < 2,
2
f (x) =
0,
otherwise.
(a) Find P (X 1).
(b) Find the cumulative distribution f
Table 1: Tabular Summary of Discrete & Continuous Distributions
Binomial
(X Bin(n, p)
pmf/pdf &
cdf, FX (t) = P (X t)
n x
pX (x) =
p (1 p)nx
x
Image &
Parameter space
E(X)
V ar(X)
2
X = cfw_0, 1, 2, , n
E(X) = np
0p1
Var(X) = np(1 p)
cdf, FX (t) = P (
Spring 2016
Statistics 322
Practice problems for Exam 2
1. A continuous random variable X has the following probability density function (pdf):
1
x, for 0 < x < 2,
2
f (x) =
0,
otherwise.
(a) Find P (X 1).
(b) Find the cumulative distribution function of