Basic Concepts in Statistics
Population, Sample,
Parameters, and Statistics
Definition: Population, Parameter, Sample
A population refer to the entire set of ind...
Generating Functions
We may use generating functions to characterize sequences.
Definition: Generating Function
The generating function for the sequence of real ...
Linear Recurrence Relations
Linear Homogeneous
Recurrences
Definition: Linear Homogeneous Recurrence Relation
A linear homogeneous relation of degree 4k$ with co...
Monte Carlo Methods
Introduction and Theoretical
Basis
Monte Carlo methods, or Monte Carlo experiments,
are a board class of computational algorithms that rely on repeated
random sampling to o...
Counting
Counting is the process of determining the number of some
objects with certain properties.
The Sum Rule and The Product
Rule
Example
the number of s...
Joint Distributions
Random Vector and Joint
Distribution
Definition: Random Vector
We say that is a
random vector if
is a function valued on , can also be
...
Mathematical Induction
Proof by Smallest
Counterexample
The statement is true for
all , we prove this
by
Assume that a counterexample exists, i.e., .
Let be the smallest
value for which...
Applications of Number
Theory
Pseudorandom Number
Generators
We will mainly introduce the linear congruential method. We
choose four numbers:
the modulus
multiplier
increment
seed
...
Data Modification
UPDATE
UPDATE is the command to changes column values, the
change is applied to all rows selected by the WHERE clause:
12345UPDATE table_nameSET column_name = new_value other_...
Elementary Data Structures
Dynamic sets that can store and retrieve elements. Data
structures are techniques for representing finite dynamic sets of
elements.
Each element can contain:
a key...
