Get Math Help

GET TUTORING NEAR ME!

By submitting the following form, you agree to Club Z!'s Terms of Use and Privacy Policy

    Limit Theorem

    Alternate name
    Basic definition

    The central limit theorem states that any set of variates with a distribution having a finite mean and variance tends to the normal distribution. This allows statisticians to approximate sets of data with unknown distributions as being normal.

    Detailed definition

    Let X_1, X_2, ..., X_N be a set of N independent random variates and each X_i have an arbitrary probability distribution P(x_1, ..., x_N) with mean μ_i and a finite variance σ_i^2. Then the normal form variate
X_norm congruent ( sum_(i = 1)^N x_i - sum_(i = 1)^N μ_i)/sqrt( sum_(i = 1)^N σ_i^2)
has a limiting cumulative distribution function which approaches a normal distribution.
Under additional conditions on the distribution of the addend, the probability density itself is also normal with mean μ = 0 and variance σ^2 = 1.

    Educational grade level

    college level (AP statistics, California probability and statistics standard)

    Find the right fit or it’s free.

    We guarantee you’ll find the right tutor, or we’ll cover the first hour of your lesson.