## table of contents

Statistics for Programmers-Table of Contents

## Overview

It is a memo of the definition of the word about "event".

## Event

An event is what happens as a result of an attempt.
For example, the result of an experiment (trial) on what to roll a dice is called an event.

## All events

All possible events.
Often represented by omega.

Example) All events when throwing dice

```
\Omega = \{1, 2, 3, 4, 5, 6\}
```

## Complex event

Events that can be decomposed

Example) An event in which an even number appears by rolling the dice
This is a compound event because it can still be decomposed into 2,4,6.

```
G = \{2, 4, 6\}
```

## Elementary event

Events that cannot be decomposed any further

Example) In the case of dice, each of the 1st to 6th rolls is an elementary event.

## Complementary event

"Except when there is" event

Example) When the event that an even number appears by rolling the dice is A, the odd numbered roll becomes a complementary event as shown below.

```
A^c = \{1, 3, 5\}
```

When the complementary events and compound events are added, it becomes all events.

```
\Omega = A + A^c = {1, 2, 3, 4, 5, 6}
```

## Empty event

An event that does not exist.
Speaking of dice, a 7 is rolled.

## Mutual exclusivity

An event that cannot occur at the same time. You can have odd-numbered eyes and even-numbered eyes at the same time.

## Sum event

Of the two events A and B, the event where ʻA or B` occurs

The formula is as follows.
A or B

```
A ∪ B
```

`∪`

is called a" cup ".

Example) An event in which an even number or a dice can be divided by 3

```
G = {2, 3, 4, 6}
```

## Product event

Of the two events A and B, events where A and B occur at the same time

The formula is as follows.
A and B

```
A ∩ B
```

`∩`

is called a hat.

Example) An even number of dice that can be divided by 3

```
G = {6}
```

## reference

-What is an event