Starnes, UPDATED The Practice of Statistics, 6e, Chapter 5

random process

Generates outcomes that are determined purely by chance.

probability

The probability of any outcome of a random process is a number between 0 and 1 that describes the proportion of times the outcome would occur in a very long A trial is one repetition of a random series of trials.

law of large numbers

Says that if we observe more and more trials of any random process, the proportion of times that a specific outcome occurs approaches its probability.

simulation

Imitates a random process in such a way that simulated outcomes are consistent with real-world outcomes.

probability model

A description of some random process that consists of two parts: a list of all possible outcomes and the probability for each outcome.

sample space

The list of all possible outcomes.

event

Any collection of outcomes from some random process.

Complement rule, Complement

The "complement rule" says that 𝑃(Aᶜ)=1−𝑃(A), where Aᶜ is the "complement" of event A; that is, the event that A does not occur.

mutually exclusive (disjoint)

Two events A and B are "mutually exclusive (disjoint)" if they have no outcomes in common and so can never occur together—that is, if 𝑃(A and B) = 0.

Addition rule for mutually exclusive events

For A and B says that 𝑃(A or B) = 𝑃(A) + 𝑃(B)

general addition rule

If A and B are any two events resulting from some random process, the "general addition rule" says that 𝑃(A or B) = 𝑃(A) + 𝑃(B) − 𝑃(A and B)

Venn diagram

Consists of one or more circles surrounded by a rectangle. Each circle represents an event. The region inside the rectangle represents the sample space of the random process.

intersection

The event “A and B” is called the "intersection" of events A and B. It consists of all outcomes that are common to both events, and is denoted A∩B.

union

The event “A or B” is called the "union" of events A and B. It consists of all outcomes that are in event A or event B, or both, and is denoted A∪B.

conditional probability

The probability that one event happens given that another event is known to have happened. The "conditional probability" that event A happens given that event B has happened is denoted by 𝑃(A|B).

independent events

A and B are independent events if knowing whether or not one event has occurred does not change the probability that the other event will happen. In other words, events A and B are independent if 𝑃(A|B) = 𝑃(A|Bᶜ) = 𝑃(A). Alternatively, events A and B are independent if 𝑃(B|A) = 𝑃(B|Aᶜ) = 𝑃(B)

general multiplication rule

For any random process, the probability that events A and B both occur can be found using the "general multiplication rule": 𝑃(A and B)= 𝑃(A∩B) = 𝑃(A) * 𝑃(B|A)

tree diagram

Shows the sample space of a random process involving multiple stages. The probability of each outcome is shown on the corresponding branch of the tree. All probabilities after the first stage are conditional probabilities.

Multiplication rule for independent events

If A and B are independent events, the probability that A and B both occur is 𝑃(A and B) = 𝑃(A∩B) = 𝑃(A) * 𝑃(B)