
Textbook:
S. Ghahramani, "Fundamentals
of Probability with Stochastic Processes, 3rd Ed," Pearson Prentice Hall, 2005.


Prerequisite: Calculus I & II


Class goals:

Learning the probability theory that
describes random phenomena


Learning probability laws and theorems for
computing probabilities of events


Learning probability methods of solving
problems



Class hours and room:
3CD5G / EC122


Office hours:
1:302:300pm
(Tuesday), 1:303:00pm (Friday)
, or by appointment via emails 

TAs &
TA office hours: at EC 229A

Amir Rezapour (ce.a.rezapour@gmail.com): 3EF, 4EF


Henry Hong (洪顥恆,
henry199442.cs01@g2.nctu.edu.tw) 1B, 2C



Grading:
(tentative)

Quizzes (in class,
several times): 15%


Homeworks: 20%


Midterms (twice) 40%


Final 25%



Syllabus

Preface [slides]


Axioms of probability
[slides] [noted
slides]

Sample
space and events


Axioms of
probability


Basic
theorems



Combinatorial methods
[slides] [noted
slides, 9/20/17]

Counting
principle


Permutation


Combinations



Conditional probability and independence
[slides]

Conditional probability


Law of
multiplication


Law of
total probability


Bayes'
formula


Independence



Distribution functions and discrete random variables

Random
variables


Distribution functions


Discrete
random variables


Expectations of discrete random variables


Variance
and moments of discrete random variables


Standardize random variables



Special discrete distributions

Bernoulli
and binomial random variables


Poisson
random variables



Continuous random variables

Probability density functions


Density
function of a function of a random variable


Expectations and variances



Special continuous distribution

Uniform
random variables


Normal
random variable



Bivariate distributions

Bivariate
distribution


Independent random variables


Conditional distributions



More expectations and variances

Expected
values of sums of random variables


Covariance


Correlation



Sums of
independent random variables and limit theorem

Markov
and Chebyshev inequalities


Law of
large numbers


Central
limit theorem


