COMP. 233.
ASSIGN. 1.
1. How many bit strings of length 10 containing at least 5 consecutive
0s or at least 5 consecutive 1s are there?
2. A Palindrome is a string whose reversal is identical to the original
string.
How many bit stings of length N are Pal
Assignment 1
29/09/2016 10:53 PM
COMP 233 Probability and Statistics for Computer Science
Fall 2016, Assignment 1
Due: September 30, 2016
Question 1:
Four bits are transmitted over a digital communications channel. Each bit is received either
distorted or
Food for Thought - 1
Suppose the joint density function of
given by
2e x e 2 y 0 < x, 0 < y
f ( x, y ) =
0
otherwise
Compute
(a) Pcfw_X>1, Y<1
(b) Pcfw_X<Y
1
COMP 233 Week 3
X and Y is
Food for Thought - 2
Decide if the following is the joint density
fu
Assignment 2
30/09/2016 4:35 PM
COMP 233 Probability and Statistics for Computer Science
Fall 2016, Assignment 2
Due: October 14, 2016
Question 1
A lot containing 7 components is sampled by a quality inspector; the lot contains
4 good components and 3 def
LECTURE NOTES
on
PROBABILITY and STATISTICS
Eusebius Doedel
TABLE OF CONTENTS
SAMPLE SPACES
Events
The Algebra of Events
Axioms of Probability
Further Properties
Counting Outcomes
Permutations
Combinations
1
5
6
9
10
13
14
21
CONDITIONAL PROBABILITY
Indep
Problem Set #4 ANSWERS
Write out answers to the following questions. If you answered the problem
in Excel, you should printout graphs and tables and attach them or insert them
into your homework. Show all work, even if you used excel you should at least
t
Continuous random variables
So far we have been concentrating on discrete random variables, whose distributions are not
continuous. Now we deal with the so-called continuous random variables.
A random variable X is called a continuous random variable if i
bl 1. ‘
Pro 3111 wl'wJ'U-lgl {L;,l¢.13
Two balls are selected at random from a bag with t ree white ba ls and two black balls.
For each of the following enter the probability in the accompanying box.
{ o The probability the ﬁrst ball is white.
0 The proba
BASIC FORMULAS
Name
Formula
P (F |E) = P (E|F )P (F ) / [ P (E|F )P (F ) + P (E|F c )P (F c ) ]
Bayes
Method of Moments
If (t) = E[etX ] then (0) = E[X] and (0) = E[X 2 ]
Markovs Inequality
For continuous, nonnegative X, c > 0 : P ( X c ) E[X] / c
Chebysh
COMP 233, Winter 2016
CONCORDIA UNIVERSITY
PROBABILITY AND STATISTICS FOR COMPUTER SCIENCE.
Assignment 1. Solutions.
1. (6 points) Suppose the sample space consists of all seven-letter words having distinct
alphabetic characters.
(a) How many words are th
Solution
Assignment 2
27/10/2015 11:42 AM
COMP 233 Probability and Statistics for Computer Science
Fall 2015, Assignment 2
Due: October 16, 2015
Question 1 The time for an older machine to do a quality check on a newly manufactured tire,
, has mean of 65
Solution
Assignment 1
06/10/2015 11:40 AM
COMP 233 Probability and Statistics for Computer Science
Fall 2015, Assignment 1
Due: Friday, Oct 2, 2015
Question 1 A carton of 12 rechargeable batteries contains two batteries that are defective.
(a) In how many
Solution
Assignment 3
13/11/2015 10:23 AM
COMP 233 Probability and Statistics for Computer Science
Fall 2015, Assignment 3
Due: November 20, 2015
Question 1 The following table gives the number of commercial airline accidents in the United
States in the y
Solution
Assignment 4
23/11/2015 7:53 PM
COMP 233 Probability and Statistics for Computer Science
Fall 2015, Assignment 4
Due: Monday, December 7, 2015
Question 1 A colony of laboratory mice consists of several thousand mice. The average weight
of all the
Formulae and Probability Tables for COMP233 Midterm Exam
Useful Facts and Formulae
1. Basic combinations: (
)
(
2. The binomial theorem: (
)
)
3. DeMorgans laws: (
)
( )
(
)
General Probability
1. Classical probability: If
is an event in
(finite, with equ
9/22/2016
COMP 233/2
Probability and Statistics
for Computer Science
Week 3 (slides curtsey Dr. T. Fevens)
S. P. Mudur
Random variable
Probability mass function
Probability density function
Cumulative distribution function
Joint probability mass function
9/29/2016
COMP 233/2
Probability and Statistics
for Computer Science
Week 4 (slides curtsey Dr. T. Fevens)
S. P. Mudur
Expectation
Properties of Expectation
Variance
Covariance
Chebyshevs inequality
Reading: 4.4-4.7, 4.9
Information About Calculators
Duri
10/6/2016
COMP 233/2
Probability and Statistics
for Computer Science
Week 5 (slides curtsey Dr. T. Fevens)
S. P. Mudur
Bernoulli and Binomial random variable
Poisson random variable
Exponential random variable
Uniform random variable
Reading: 5.1-5.2, 5.4
COMP. 233.
Probability and Statistics for Computer Science.
1. General Information.
COMP. 233: Probability and Statistics for Computer Science (3 credits).
2. Course Description.
This course introduces Probability and Statistics for computer science stude
COMP. 233.
W
1. Three balls are randomly selected without replacement from an urn
containing 20 balls numbered 1 through 20. If we bet that at least one of
the drawn balls has a number greater than 'or equal to 17, what is the
probability that we win the
Bernoulli Distribution
Binomial Distribution
Hypergeometric Distribution
Geometric Distribution
Negative Binomial Distribution
Poisson Distribution
Uniform Distribution
Exponential Distribution
Normal Distribution
Chi-Square Distribution
T - Distribution
COMP. 233.
ASSIGN. 3.
1. A certain small freight elevator has a max. capacity C, which is Normally
distributed, with mean 400 lbs., and standard deviation 4 lbs.
The weight of the boxes being loaded into the elevator is a R.V., with
mean 30 lbs., and stan
COMP. 233.
ASSIGN. 4.
1. Find the Maximum Likelihood Estimator for from the Exponential
Distribution:
f(x) =
2. Find the Maximum Likelihood Estimator for p from the Binomial
Distribution:
P(x) =
px (1 - p)N x
3. An Argentinean Rancher, who raises miniatu
COMP. 233.
ASSIGN. 5.
3 pages.
1. A Real Estate Broker who is anxious to sell a piece of property to a motel
chain assures them that during the summer months, on the average, 4,200
cars pass by the property per day. Being suspicious that this figure might
Assignment 1
12/09/2016 4:47 PM
COMP 233 Probability and Statistics for Computer Science
Fall 2016, Assignment 1
Due: September 30, 2016
Question 1:
Four bits are transmitted over a digital communications channel. Each bit is received either
distorted or
COMP 233 Probability and Statistics for Computer Science
Time: TJ 13h15-14h30 (Lect) in H920 and 10h15-11h55 (Tut) T H523- QA /J H523-QB
Instructor: Sudhir Mudur, Dept. of CSE, ENCS (office EV 3.159)
Means of Contact: Email: mudur@cs.concordia.ca (preferr
9/15/2016
COMP 233/2
Probability and Statistics
for Computer Science
Week 2 (slides curtsey Dr. T. Fevens)
S. P. Mudur
Conditional probability,
Bayes formula,
Independent events
Reading: 3.6-3.8
Food for thought
A student is taking a Data Structures test
Food for Thought Example 1
In answering a question on a multiple-choice test,
a student either knows the answer or she guesses.
Let p=0.6 be the probability that she knows the
answer and 1p = 0.4 be the probability that she
guesses.
Assume that a studen
10/11/2016
COMP 233/2
Probability and Statistics
for Computer Science
Week 6 (slides curtsey Dr. T. Fevens)
S. P. Mudur
Normal random variables
Chi-square distribution
t-distributions
Reading: 5.5, 5.8
Food for Thought
An oil company conducts a geologica
Food for Thought
We can use the Chebyshev inequality to prove the
Weak Law of Large Numbers.
That is use the Chebyshev inequality,
Pcfw_ X k
Var ( X )
k2
And prove:
X1 + L + X n
P
> 0 as n
n
COMP233 Week 4
1
Food for Thought
A representative from