Random Variables

Flashcards covering vocabulary from lecture notes on random variables, discrete and continuous random variables, transformations, binomial and geometric random variables.

Random Variable

A numerical variable that describes the outcomes of a chance process.

Probability Distribution

The probability model for a random variable; it gives its possible values and their probabilities.

Discrete Random Variable

A random variable that takes a fixed set of possible values with gaps between.

Continuous Random Variable

A random variable that takes on all values in an interval of numbers.

Mean of a Discrete Random Variable

An average of the possible outcomes, with each outcome weighted by its probability. Also known as expected value.

Variance of a Discrete Random Variable

The average squared deviation of the values of the variable from their mean.

Standard Deviation of a Discrete Random Variable

The square root of the variance of a discrete random variable.

Linear Transformation

Transformation of a random variable using the form Y = a + bX, where a and b are constants.

Independent Random Variables

Knowing whether any event involving X alone has occurred tells us nothing about the occurrence of any event involving Y alone, and vice versa.

Binomial Setting

Arises when we perform several independent trials of the same chance process and record the number of times that a particular outcome occurs. (BINS: Binary, Independent, Number, Success)

Binomial Random Variable

The count X of successes in a binomial setting.

Binomial Coefficient

The number of ways of arranging k successes among n observations.

Geometric Setting

Arises when we perform independent trials of the same chance process and record the number of trials until a particular outcome occurs. (BITS: Binary, Independent, Trials, Success)

Geometric Random Variable

The number of trials Y that it takes to get a success in a geometric setting.