1.1 Sample space and events

1.1.1 Introduction to sample space

Definition:

e.g. Rolling a dice

• experiment: rolling the dice
• outcome: the result of experiment (a number in 1~6)
• sample space($\Omega$): all possible outcome of the experiment (1~6)

Examples:

1.1.2 Set Operations

Definition:

Let $\Omega$ be a given sample space and $E,F\subset\Omega$ are 2 events.

• $E \cup F := \{x\in\Omega:x\in E\ or\ x\in F\}$
  • The union of $E,F$. (either one of them occurs)
• $E \cap F := \{x\in\Omega:x\in E\ and\ x\in F\}$:
  • $E \cap F$ equals $EF$. ( both they two occur)
  • The intersection of $E,F$.
• $E^c := \{x\in\Omega:x\notin E\}$
  • The complement of $E$. ( the negation of $E$, $E$ doesn’t occur)

• Null event: $\empty$, consisting no outcomes.
• If $E \cap F = \empty$, then they’re mutually exclusive or disjoint events.