[PYTHON] [Statistics for programmers] What is an event?

table of contents

Statistics for Programmers-Table of Contents


It is a memo of the definition of the word about "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}


-What is an event

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