Continuous CLT

A learning component illustrating the Central Limit Theorem (CLT) for a chosen continuous distribution.

Options

distributions | array<string>: statistical distributions to choose from ('uniform', 'exponential', and/or 'normal'). Default: [ 'uniform', 'exponential', 'normal' ].
samples | (array<number>|number): array of numbers or a single numbers denoting the sample sizes that can be drawn. Default: 25.
hideFormulas | boolean: controls whether to hide formulas in the component text. Default: false.

Live Editor

<LearnContinuousCLT />

<LearnContinuousCLT />

Result

Minimum

a

Maximum

b

Rate parameter

λ

Mean

μ

Standard deviation

σ

Active Distribution:

Uniform (a Minimum = 0, b Maximum = 1)

Population mean: $\frac{1}{2} (a + b) = 0.500$

Population standard deviation: $\frac{1}{\sqrt{12}} | b - a | = 0.289$

Sample Size:

Number of Samples: 0

Histogram of

\bar{x}

Please draw at least two samples.

Overlay normal density

\bar{x}

Values

x

P (X < 0) = 0.000

P (X \geq 0) = 1.000

P (L = - I n f i n i t y < X < U = I n f i n i t y) = 1.000

\bar{x}

P (\bar{X} < 0) = 0.000

P (\bar{X} \geq 0) = 1.000

P (L = - I n f i n i t y < \bar{X} < U = I n f i n i t y) = 1.000