JBM015 Data Statistics Lecture 1: Random Experiments

Random Experiments and Events

• In a random experiment, the set of all possible outcomes is called the sample space.

Throwing a Fair Die

• The sample space of throwing a fair die is {1, 2, 3, 4, 5, 6}.

Events

• In the context of random experiments, events are subsets of the sample space.

Sample Space Example

• The sample space {RR, RC, RS, CR, CC, CS, SR, SC, SS} represents the outcomes of tossing two coins, where R is heads and S is tails.

Event Example

• When playing a board game, the event A is rolling 4 or above to win.

Empty Event

• The empty set, denoted by ∅, represents an empty event.

Partition of Subsets

• A partition of subsets D1,..., Ds of Ω entails that every outcome in Ω belongs to exactly one of the subsets Di.

Classical Definition of Probability

• The classical definition of probability applies when all outcomes in the sample space are equally likely.

Probability of Sample Space

• Under the classical definition, P(Ω) represents 1, or certainty.

Probability of Disjoint Events

• Under the classical definition, if events A and B are disjoint, P(A ∪ B) is the sum of P(A) and P(B).