Engineering Statistics - Joint Distributions

These flashcards cover key vocabulary and definitions from the lecture on joint distributions in engineering statistics.

Joint Distribution Function (CDF)

The joint cumulative distribution function (CDF) of a random vector is the probability of the vector being less than or equal to certain values.

Marginal Distribution Function

The marginal distribution function gives the probability distribution of a subset of multivariate random variables.

Covariance

A measure of the joint variability of two random variables. It indicates the direction of the linear relationship between them.

Conditional Probability Density Function (PDF)

The probability density function of a random variable given that another variable is fixed at a specific value.

Independent Variables

Random variables are independent if the occurrence of one does not affect the probability of occurrence of the other.

Mean of a Random Variable

The expected value or average of a random variable.

Central Limit Theorem (CLT)

A statistical theory that states that the distribution of sample means approaches a normal distribution as the sample size increases.

Joint CDF Properties

Properties include: 0 ≤ F(x,y) ≤ 1, limit behaviors at infinities, and reduction to marginal CDFs.

Random Vector

A vector composed of multiple random variables, each of which can vary in nature.

Joint Probability Density Function (PDF)

A function that represents the probability that each of the random variables falls within a specified range.

Mean of Function of Random Variables

The expected value of a function defined in terms of random variables.

Law of Large Numbers

The principle that as the size of a sample increases, its sample mean will converge to the expected value.

Random Sample

A subset of individuals chosen from a larger set, where every individual has an equal chance of being selected.

Correlation Coefficient

A statistical measure that indicates the extent to which two variables fluctuate together.

Cumulative Distribution Function (CDF)

A function that specifies the probability that a random variable will take a value less than or equal to a certain level.

Joint Probability Mass Function

A function that gives the probability of discrete multivariate random variables.

Marginal Probability Mass Function

The probability mass functions of individual discrete random variables from a joint distribution.

Normalization Condition for PDF

The requirement that the total probability across the entire space equals 1.

Integration in Joint Distributions

The process of calculating joint probabilities by integrating marginal distributions.

Disjoint Events

Events that cannot occur simultaneously; the occurrence of one event excludes the other.

Marginalization

The process of summing or integrating over one or more variables in a joint distribution to obtain a marginal distribution.