Introduction to Probability

_Part One

Experiment: An activity or process that has specific results that can be repeated indefinitely which has a set of well-defined outcomes.
Outcomes: The results of an experiment.
Sample Space: Collection of all possible outcomes of the experiment. Usually denoted as S.
Event: The set of outcomes that are a subset of the sample space. The symbol used for events is usually a capital letter often at the beginning of the alphabet, like A, B or C.
Probability Rules: The probability of an event A must be between o and 1, inclusive.; P(S) = 1 where S is the sample space.
Complement Rule: Complement of A is denoted as A^c or A with a bar over it.; The probabilities of two complementary events both add to 1.; Complementary events are two events that have no outcomes in common and together they make up the entire sample space.

Theoretical Probability: This can only be used if each outcome has an equal probability.; P(A) = (Number of ways A can occur)/(Number of different outcomes in S).
Empirical Probability: P(A) = (Number of times A occurred)/(Number of times the experiment was repeated).

Individual

A person, case, or object that you are interested in finding information about.

Statistics

The science of conduction studies to collect, organize, summarize, analyze, and draw conclusions from data.

Descriptive Statistics Describing Data: Consists of the collection, organization, summarization, and presentation of data.
Inferential Statistics Interpreting Data: Consists of generalizing from samples to populations, performing estimations and hypothesis tests, determining relationships among variables, and making predictions. (Inferential statistics uses probability).

Data Set

A collection of data values. Each value in the data set is called a data value or datum.

Data: The values (measurements or observations) that the variables can assume. variables whole values are determined by chance are called random variables.

Population

Consists of all subjects (human or otherwise) that are being studied.

Sample

A group of subjects selected from a population.

Statistics estimates parameters.

Nominal Level of Measurement: The Nominal Level of Measurement classifies data into mutually exclusive (non-overlapping) categories in which no order or ranking can be imposed on the data.
Ordinal Level of Measurement: The Ordinal Level of Measurement classifies data into categories that can be ranked; however, precise differences between ranks do not exist.
Interval Level of Measurement: The interval level of measurement ranks data, and precise differences between units of measure do exist; however, there is no meaningful zero.
Ratio Level of Measurement: The Ratio Level of Measurement Possesses all the characteristics of interval measurement, and there exists a tru zero. In addition, true ratios exist when the same variable is measured on two different members of the population.

A characteristic or attribute that can assume different values.

Qualitative Variables Categorical Variable

Variables that have distinct categories according to some characteristic or attribute.

Nominal Variables: Name only; Color of a car
Ordinal Variables: Order matters; Has a finite number of possible outcomes.; How often do you workout? Never, sometimes, daily.; Rate you anxiety on a scale of 1-10.

Quantitative Variables Numerical Variable

Variables that can be counted or measured.

Discrete Variables: Variables with a countable, but not finite, number of possible outcomes; Only take on particular values such as integers or whole numbers.; Number of __, Shoe sizes.
Continuous Variables: They are obtained by measuring, have an uncountable number of possible outcomes.; Can assume an infinite number of values between any two specific values.; They often include fractions or decimals.; Time, distance, weight, height.