We say type A is a subtype of type B, if everything we can do with B, we can do with A. Or we say, A can be treated as

Singularity analysis provides an alternative way to anlyze the growth of generating funtion precisely. It is systematic and reliable.

The question of selecting a winner/loser is extremely easy to understand but is not at all trivial to analyze.... Here I present Prodinger's method with Rice's method.

Which is faster? ++i; or i++;   Both ++i and i++ are expression with side effects. The side effects are the same (increment i by one), but the return value

From Probability to Statistics In the world of probability, we look at the set of all possible outcomes of an experiment. This set of all possible outcomes is called sample

The following text assumes the definitions and notations used in Definitions of Markov Chain With the additional concept on period and reducibility. We denote the period of a state $i$ by

Stochastic Process Let $T$ be a set, and $\{N(t) | t \in T\}$ be a set of random variables, $\{N(t) | t \in T\}$ is called a stochastic process. If

The following text assumes the definitions and notations used in Definitions of Markov Chain Specifically, we define $P^n_{ij}$ as $[P^n]_{ij}$, which is the $i-j$th entry of the matrix $P^n$. The physical meaning