Expected Value

Introduction

The expected value E(X) is the arithmetic mean of a random variable X.

Definition

1. Let X be a discrete random variable and the range is  , then

E(X)=\sum_{x\in R_{X}}^{}xf_{x}(x)

2. Let X be a continuous random variable and the range is  , then

E(X)=\int_{x\in R_{X}}^{}xf_{x}(x)dx

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Kolmogorov Axioms

Introduction

Kolmogorov axioms or probability axioms were introduced by Soviet mathematician Andrey Kolmogorov(April 25, 1903- October 20, 1987). 

All the theorems in probability theory are derived from the axioms.

Read moreKolmogorov Axioms

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σ-algebra

Definition

σ-algebra or Borel field is a collection of subsets of a sample space S,

and it must satisfy the following three properties:

  • The empty set is an element of σ-algebra.
  • σ-algebra is closed under complementation.
  • σ-algebra is closed under countable unions.

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Sample Space

Definition

Sample space is a set of all possible outcomes of an experiment.

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Measures of Central Tendency

Introduction

Measures of central tendency are used to describe the trend of value or values in a dataset.

Related Topics

◆ Arithmetic Mean

◆ Geometric Mean

◆ Harmonic Mean

◆ Truncated Mean

◆ Mode

◆ Median

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Measures of Dispersion

Introduction

Measures of Dispersion are used to understand the scatterings of data.

Related Topics

◆ Range

Variance

◆ Standard Deviation

◆ Coefficient of Variance

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