Engineering Statistics - Continuous Random Variables

A collection of vocabulary flashcards covering key concepts related to continuous random variables in engineering statistics.

Continuous random variable

A variable that can take any real value, not finite or countable.

Probability Density Function (PDF)

A function that describes the likelihood of a continuous random variable taking a specific value.

Cumulative Distribution Function (CDF)

A function that describes the probability that a continuous random variable is less than or equal to a certain value.

Mean of a continuous random variable

The expected value, calculated as the integral of the variable multiplied by its PDF.

Variance of a continuous random variable

A measure of the spread of the variable's values, calculated from the mean.

Percentiles

Values that divide a data set into 100 equal parts, indicating the relative standing of a value.

Median

The 50th percentile; the value that separates the higher half from the lower half of the data.

Uniform distribution

A type of distribution where all outcomes are equally likely.

Normal distribution

A probability distribution that is symmetric about the mean, showing that data near the mean are more frequent.

Lognormal distribution

A distribution of a variable whose logarithm is normally distributed.

Exponential distribution

A continuous probability distribution often used to model time until an event occurs.

Gamma distribution

A two-parameter family of continuous probability distributions that generalizes the exponential distribution.

Weibull distribution

A continuous distribution used for reliability analysis and failure times.

Function of a random variable

A transformation applied to a random variable, resulting in a new random variable.

Probability plot

A graphical technique for assessing whether or not a data set follows a given distribution.

Standard continuous random variable

A variable with a uniform distribution on the interval [0,1].

Moments

Quantities that describe the shape of a probability distribution.

CDF properties

Properties that define the behavior of the CDF, such as being non-decreasing.

Normalization condition

The requirement that the total probability of all outcomes from the PDF must equal to 1.

Central limit theorem

The theorem that states the distribution of the sum of a large number of independent random variables will be approximately normal.

Uniform description of discrete and continuous variables

A framework that provides a unified approach to handle both types of variables using generalized functions.

Dirac delta function

A generalized function that models an idealized point mass or point charge.

Heaviside function

A step function used in mathematics which is zero for negative arguments and one for positive arguments.

Statistical inference

The process of drawing conclusions about populations from sample data.

Approximation of binomial distribution

Using the normal distribution to approximate the binomial distribution under certain conditions.

Boltzmann constant

A physical constant relating the average kinetic energy of particles in a gas with the temperature of the gas.

Percentiles of normal distribution

Specific points in a normal distribution indicating the value below which a given percentage of observations fall.

Three sigma rule

A statistical rule stating that, for a normal distribution, approximately 99.7% of values lie within three standard deviations of the mean.