## Shem Shen's Blog

### 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 2. Let X be a continuous random variable and the range is , then (Visited 11 times, 1 visits today)

### 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.

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### 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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### Definition

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

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### 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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### 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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### Introduction

Descriptive statistics is a study of managing and describing data properties and exchanging the data into useful information.

Related Topics

Frequency Distribution

◆ Charts

◆ Scales of Measurement

◆ Measures of Central Tendency

◆ Measures of Dispersion

◆ Skewness and Kurtosis

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### Definition

Random variables are the functions from sample space S into real numbers R.

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### What are Scales of Measurement?

Introduction

Scales of measurement or levels of measurement were developed by American psychologist Stanley Smith Stevens(November 4, 1906 – January 18, 1973).

He classified variables into four levels: nominal, ordinal, interval, and ratio.

Based on the order of four levels, the usable operators get more and more from nominal to ratio.

Read moreWhat are Scales of Measurement?

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# Statement

Let X be a non-negative random variable, and E(X) exists, c > 0, then, or Read moreHow to Prove Markov’s Inequality

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