floor function

(noun)

maps a real number to the smallest following integer

Related Terms

Examples of floor function in the following topics:

  • Additional Properties of the Binomial Distribution

    • Usually the mode of a binomial B(n, p) distribution is equal to where is the floor function.

  • Comparing Two Independent Population Means with KNown Population Standard Deviations

    • independent groups, population standard deviations known: The mean lasting time of 2 competing floor waxes is to be compared.
    • Twenty floors are randomly assigned to test each wax.
    • $\bar{X_1} - \bar{X_2}$ = difference in the mean number of months the competing floor waxes last.

  • Common Discrete Probability Distribution Functions

    • Some of the more common discrete probability functions are binomial, geometric, hypergeometric, and Poisson.
    • A probability distribution function is a pattern.

  • Continuous Probability Distributions

    • A continuous probability distribution is a probability distribution that has a probability density function.
    • In theory, a probability density function is a function that describes the relative likelihood for a random variable to take on a given value.
    • Unlike a probability, a probability density function can take on values greater than one.
    • The standard normal distribution has probability density function:
    • Boxplot and probability density function of a normal distribution $$$N(0, 2)$.

  • Continuous Probability Functions

    • We begin by defining a continuous probability density function.
    • We use the function notation f (x).
    • In the study of probability, the functions we study are special.
    • Consider the function f (x) = 1 20 for 0 ≤ x ≤ 20. x = a real number.
    • This particular function, where we have restricted x so that the area between the function and the x-axis is 1, is an example of a continuous probability density function.

  • The Density Scale

    • Density estimation is the construction of an estimate based on observed data of an unobservable, underlying probability density function.
    • The unobservable density function is thought of as the density according to which a large population is distributed.
    • A probability density function, or density of a continuous random variable, is a function that describes the relative likelihood for this random variable to take on a given value.
    • The above image depicts a probability density function graph against a box plot.
    • This image shows a boxplot and probability density function of a normal distribution.

  • Exercises

    • For the following data, plot the theoretically expected z score as a function of the actual z score (a Q-Q plot).
    • For the "SAT and College GPA" case study data, create a contour plot looking at College GPA as a function of Math SAT and High School GPA.

  • Notation for the Hypergeometric: H = Hypergeometric Probability Distribution Function X ~ H (r,b,n)

    • NOTE : Currently, the TI-83+ and TI-84 do not have hypergeometric probability functions.

  • Continuous Sampling Distributions

    • A probability density function, or density of a continuous random variable, is a function that describes the relative likelihood for this random variable to take on a given value.
    • Boxplot and probability density function of a normal distribution $N(0, 2)$.

  • Properties of Continuous Probability Distributions

    • The curve is called the probability density function (abbreviated: pdf).
    • We use the symbol f (x) to represent the curve. f (x) is the function that corresponds to the graph; we use the density function f (x) to draw the graph of the probability distribution.
    • Area under the curve is given by a different function called the cumulative distribution function (abbreviated: cdf).
    • The cumulative distribution function is used to evaluate probability as area.
    • In general, calculus is needed to find the area under the curve for many probability density functions.