discrete variable

(noun)

a variable that takes values from a finite or countable set, such as the number of legs of an animal

Related Terms

Examples of discrete variable in the following topics:

  • Probability Distributions for Discrete Random Variables

    • Probability distributions for discrete random variables can be displayed as a formula, in a table, or in a graph.
    • A discrete random variable $x$ has a countable number of possible values.
    • The probability mass function has the same purpose as the probability histogram, and displays specific probabilities for each discrete random variable.
    • This histogram displays the probabilities of each of the three discrete random variables.
    • This table shows the values of the discrete random variable can take on and their corresponding probabilities.

  • Types of Variables

    • Numeric variables may be further described as either continuous or discrete.
    • A discrete variable is a numeric variable.
    • A discrete variable cannot take the value of a fraction between one value and the next closest value.
    • Variables can be numeric or categorial, being further broken down in continuous and discrete, and nominal and ordinal variables.
    • Distinguish between quantitative and categorical, continuous and discrete, and ordinal and nominal variables.

  • Expected Values of Discrete Random Variables

    • The expected value of a random variable is the weighted average of all possible values that this random variable can take on.
    • A discrete random variable $X$ has a countable number of possible values.
    • The probability distribution of a discrete random variable $X$ lists the values and their probabilities, such that $x_i$ has a probability of $p_i$.
    • In probability theory, the expected value (or expectation, mathematical expectation, EV, mean, or first moment) of a random variable is the weighted average of all possible values that this random variable can take on.
    • The weights used in computing this average are probabilities in the case of a discrete random variable.

  • Two Types of Random Variables

    • A random variable $x$, and its distribution, can be discrete or continuous.
    • Random variables can be classified as either discrete (that is, taking any of a specified list of exact values) or as continuous (taking any numerical value in an interval or collection of intervals).
    • Discrete random variables can take on either a finite or at most a countably infinite set of discrete values (for example, the integers).
    • Examples of discrete random variables include the values obtained from rolling a die and the grades received on a test out of 100.
    • This shows the probability mass function of a discrete probability distribution.

  • Variables

    • In this case, the variable is "type of antidepressant. " When a variable is manipulated by an experimenter, it is called an independent variable.
    • An important distinction between variables is between qualitative variables and quantitative variables.
    • Qualitative variables are sometimes referred to as categorical variables.
    • Variables such as number of children in a household are called discrete variables since the possible scores are discrete points on the scale.
    • Other variables such as "time to respond to a question" are continuous variables since the scale is continuous and not made up of discrete steps.

  • Probability Distribution Function (PDF) for a Discrete Random Variable

    • This is a discrete PDF because

  • Introduction

    • These two examples illustrate two different types of probability problems involving discrete random variables.
    • Recall that discrete data are data that you can count.
    • A random variable describes the outcomes of a statistical experiment in words.
    • The values of a random variable can vary with each repetition of an experiment.
    • In this chapter, you will study probability problems involving discrete random distributions.

  • Introduction

    • Continuous random variables have many applications.
    • The field of reliability depends on a variety of continuous random variables.
    • NOTE: The values of discrete and continuous random variables can be ambiguous.
    • For example, if X is equal to the number of miles (to the nearest mile) you drive to work, then X is a discrete random variable.
    • How the random variable is defined is very important.

  • The Hypergeometric Random Variable

    • A hypergeometric random variable is a discrete random variable characterized by a fixed number of trials with differing probabilities of success.
    • The hypergeometric distribution is a discrete probability distribution that describes the probability of $k$ successes in $n$ draws without replacement from a finite population of size $N$ containing a maximum of $K$ successes.
    • A random variable follows the hypergeometric distribution if its probability mass function is given by:

  • Types of variables

    • For this reason, the population variable is said to be discrete since it can only take numerical values with jumps.
    • A variable with these properties is called an ordinal variable.
    • To simplify analyses, any ordinal variables in this book will be treated as categorical variables.
    • Classify each of the variables as continuous numerical, discrete numerical, or categorical.
    • Because the number of siblings is a count, it is discrete.