STA 4821 Stochastic Models for Computer Science
(Aka: Probability and Statistics for CS)
Last modified: 16Jul98 by R.Levow
New and updated items
Exam 4 and last homework
Class Time: Thursday, 6:30 - 10:10 pm, LA-333 (Davie)
Textbook: Probability and Statistics for Engineering
and the Sciences, 4/e, by Jay L. Devore, Duxbury Press, 1995.
Prerequisite: MAC 2312 Calculus II
Catalog Description: Basic principles of probability and statistics
for modeling and experimentation in computer science. Topics from probability
and statistics include basic concepts, conditional probability, random
variables, distribution and density functions, stochastic processes, the
central limit theorem, and simulation; applications include computer system
performance evaluation, fault-tolerant computing, software reliability,
telecommunications traffic analysis.
Course Outline
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Introduction and Descriptive Statistics
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Overview of Probability and Statistics
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Descriptive Statistics
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Measures of Location and Variability
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Probability
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Sample Spaces and Events
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Axioms and Properties
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Counting Techniques
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Conditional Probability and Independence
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Discrete Random Variable and Probability Distributions
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Random Variables and Distributions
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Expected Value
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Binomial, Hypergeometric, Negarive Bionmial, and Poisson Distributions
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Continuous Random Variables and Probability Distributions
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Continuous Random Variables and Probability Density Functions
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Dumulative Distribution Functions and Expected Value
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Normal and Gamma Distributions
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Joint Probability Distributions and Random Samples
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Jointly Distributed Random Variables
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Expected Values, Covariance, and Correlation
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Statistics and Their Distributions
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Distribution of the Sample Mean
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Distribution of a Linear Combination
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Point Estimation
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Statistical Intervals Based on a Single Sample
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Hypothesis Testing Based on a Single Sample
Reading Assignments, Exercises, and Exam Schedule
May 21: Chapters 1 (except boxplots) & 2
Exercises: Ch.1: 25, 31, 37, 39, 64;
Ch. 2: 3, 7, 11, 13, 19, 23, 33, 35, 37, 51, 57, 59, 71, 73
May 28: Chapter 3
Exercises: Ch. 3: 7(a-d), 9a, 13, 17,
23, 29, 31(a-c), 35, 45(a,c,e), 49, 51, 63, 69, 91, 95
June 4: Chapter 4 sections 1 and 2 -- Taped lecture
Exercises: Ch. 4: 1, 5, 11, 15
Tape is also available at Library Media Center (Boca Campus) and may
be in the Davie Library
June 11: Exam review; Chapter 4, section 3 (skipping sections 4 - 6)
Exercises: Ch. 4: 26ace, 27abd, 33, 37, 49
June 18: Exam 1 on Chapters 1, 2, 3
June 25: Chapter 5, Sections 1 - 2
Exercises: Ch. 5: 3bd, 5ab, 9abe, 23, 25,
31
July 2: Chapter 5, Section 3 - 5
Exercises: Ch. 5: 45, 49, 53
July 9: Exam 2 Chapters 4 and 5 (topics)
followed by lecture on Chapter 6
Exercises: Ch. 6: 1, 7, 25
July 16: Chapter 7
Exercises: Ch. 7: 1, 3, 11, 17, 21, 27
July 23: Exam 3 on Chapters 6 and 7 followed by lecture on Chapter
8
Homework
to be collected July 23: Ch 6: 8, 14; Ch. 7: 4, 12, 18, 22,
24
July 30: Chapter 9 (continued)
August 6: Exam 4 on chapter 8, sections 1-3 
Homework to be collected August 6:
Ch. 8: 4, 10abc, 28, 34
Homework
Suggested problems from the text will be assigned on a regular basis.
In general, these will be discussed at the beginning of the following
class but they will not be collected. Problems on exams will often
be based on the assigned problems. A few homework assignments will
be designated as graded assignments and will be collected.
Grading
The final grade will be computed using roughly these weightings:
Homeworks 10%; Exams 1, 30%; Exams 2, 3, and 5, 20%
Exam 2 Topics
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From Chapters 1 - 3, only definitions and material from problems on Exam
1
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From Chapters 4 (sections 1 - 3) and Chapter 5
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Definitions:Continuous random variable (crv), probibility distribution,
probabiliby density funciton (pdf), uniform distribution, cumulative distribution
function(cdf), median of a crv, expected value, variance, and standard
deviation of a crv, shape of graph of normal distribution, z-sub-alpha,
joint pmf and pdf, marginal distribution, independent random variable,
conditional distribution, expected value, covairance, correlation, statistic,
sampling distribution, random sample, central limit theorem (CLT)
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Topics: Probability of a single point and of an interval; relationship
between pdf, cdf, and probability of an interval; computation of mean,
variance, and standard deviation of a crv; relationship between normal
distribution and standard normal distribution; normal approximation to
the binomial distribution; exact conditions for using each approximation
to the binomial distribution; calculation of probabilities for joint distributions,
marginal distribution, conditional distribution, expected value, covairance,
correlation; linearity and bounds on correlation; meaning of correlations
0, 1, and -1; facts about distribution of sample mean in general and for
normal distributions; when to apply CLT