STAT 1000 - Probability & Sampling Distribution of the Sample Mean

Flashcards covering key vocabulary and definitions from the lecture notes on Probability and Sampling Distribution.

Probability

The branch of mathematics that describes random behavior.

Random Behavior

Unpredictable short-term outcomes that show regular distributions in the long run.

Sample Space

The set of all possible outcomes of a random phenomenon.

Central Limit Theorem

States that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases.

Random Experiment

A process or activity with uncertainty leading to two or more possible outcomes.

Probability Distribution

A function that describes the likelihood of obtaining the possible values of a random variable.

Discrete Random Variable

A variable that has a countable number of possible outcomes.

Continuous Random Variable

A variable that can take all possible values in an interval.

Event

Any subset of outcomes in the sample space.

Complement

The event consisting of all outcomes in the sample space which are not contained in a specified event.

Proportion vs Probability

Proportion is an observed value, probability is a theoretical value regarding future events.

Random Variable

A variable whose value is a numerical outcome of a random phenomenon.

Histogram

A graphical representation of the distribution of data.

Mathematical Model

An abstract model that uses mathematical language to describe the behavior of a system.

Long-run Behavior

The behavior of outcomes over a large number of trials.

Normal Distribution

A continuous probability distribution characterized by a symmetric bell-shaped curve.

Mean of Sampling Distribution

The mean of the sample means is equal to the population mean.

Standard Deviation of Sampling Distribution

The standard deviation of the sample means is equal to the population standard deviation divided by the square root of the sample size.

Probability of Outcome

The likelihood of a specific outcome occurring in a random experiment.

Infinity in Trials

The theoretical concept of conducting an infinite number of trials to determine probabilities.