Statistics CH4- Introduction to probability

Probability

is a numerical value that measures the likelihood that an event occurs.
• Between zero (0) and one (1).
• Probability = 0: impossible event.
• Probability = 1: definite event

Experiment

is a process that leads to one of several possible outcomes

Exhaustive events

• All possible outcomes of an experiment belong to the events.

• Include all outcomes in the sample space

Mutually exclusive events

• Do not share any common outcomes.

• The occurrence of one event precludes the occurrence of others.

Intersection of two events

Denoted A^B
• The portion in the Venn diagram
• that is included in both A and B.
• All outcomes in A and B.

Complement of an event

Denoted A^c
• The portion in the Venn
diagram including
everything in S that is not
included in A.
• All outcomes in the
sample space S that are
not in A

Subjective method for assigning a probability

calculated by drawing on personal and subjective judgement.

Empirical method

calculated as a relative frequency of occurrence.

Classical method

based on logical analysis rather than on personal judgment or observation

Law of large numbers

The empirical probability approaches the classical probability if the
experiment is run a very large number of times.

Contingency table

• is useful when examining the
  relationship between two categorical variables.

• It shows the frequencies for two categorical variables, x
  and y.

• Each cell represents a mutually exclusive combination of
  the pair of x and y observations.

• We can estimate empirical probabilities by calculating the
  relative frequencies of occurrence of relevant events.

Total probability rule

is a useful tool for breaking the computation of a probability into distinct cases.

Bayes’ theorem

uses total probability rule to update the probability of an event that has been affected by a new piece of evidence