I. Basic math.
 II. Pricing and Hedging.
 III. Explicit techniques.
 IV. Data Analysis.
 1 Time Series.
 2 Classical statistics.
 A. Basic concepts and common notation of classical statistics.
 B. Chi squared distribution.
 C. Student's t-distribution.
 D. Classical estimation theory.
 E. Pattern recognition.
 3 Bayesian statistics.
 V. Implementation tools.
 VI. Basic Math II.
 VII. Implementation tools II.
 VIII. Bibliography
 Notation. Index. Contents.

## Basic concepts and common notation of classical statistics.

collection of independent and identically distributed (iid) random variables with distribution is called a random sample from population .

Let be a real valued function whose domain includes the sample space of . The random variable is called "statistic".

Sample mean and variance are ,

The following identity is useful for any numbers

For any sample of population with mean and finite variance the sample mean and variance have the properties .

 Notation. Index. Contents.