ISDS exam 2

Probability

The numerical measure of how likely an event is to occur, ranging from 0 to 1.

Experiment

A process that generates outcomes, such as flipping a coin or drawing a card.

Sample Space (S)

The set of all possible outcomes of an experiment

Event

a subset of the sample space consisting of one or more outcomes

exhaustive events

a group of events that together include all possible outcomes in the sample space.

Mutually exclusive events

events that cannot occur at the same time.

If A and B are mutually exclusive:

P(A ∩ B) = 0

Union of two events (A ∪ B) means:

The event that A occurs OR B occurs OR both occur

Intersection of Two Events (A ∩ B)

The event that A and B occur at the same time.

Complement of an Event (Aᶜ)

The event that A does NOT occur

complement rule

P(Aᶜ) = 1 − P(A)

Addition Rule

P(A ∪ B) = P(A) + P(B) − P(A ∩ B)

Addition Rule if events are mutually exclusive

P(A ∪ B) = P(A) + P(B)

Conditional Probability

The probability that event A occurs given that event B has already occurred.

Independent events

Two events are independent if:

P(A|B) = P(A)

or

P(B|A) = P(B)

Multiplication Rule for Independent Events

If A and B are independent:

P(A ∩ B) = P(A)P(B)

Normal Distribution

A symmetric, bell-shaped distribution where the mean, median, and mode are equal

Standard normal distribution

A normal distribution with:

Mean = 0

Standard Deviation = 1

Z-score

the number of standard deviations a value if from the mean.

Probability sample

A sample where every population member has a known probability of being selected.

Non-probability sample

A sample where some members of the population have no change of being selected

inferential statistics

using sample data to draw conclusions about a population

Sampling distribution of the mean

the probability distribution of all possible sample means

standard error

the standard deviation of the sampling distribution

Central Limit Theorem

The sampling distribution becomes approximately normal when sample size is large (n>30)