Statistics
Set Theory
Permutations & Combinations
Probability Theory
Distributions
  Discrete Systems
    Binomial
      Binomial Plot
    Hypergeometric
      Hypergeometric Plot
    Poisson
      Poisson Plot
  Continuous Systems
    Normal
      Normal Plot
    Uniform
      Uniform Plot
    Exponential
      Exponential Plot
Reliability
Least Squares
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Normal Distribution

The normal distribution, or Gaussian distribution, is a symmetrical distribution commonly referred to as the bell curve. It can be considered as a special case of the binomial distribution with a very large number of trials (n is inf) and an equal success/failure rate (p=q=0.5).

Suppose that the mean value and standard deviation of a normal distribution are mu and sigma, respectively. The normal distribution has the following important properties. See plots of normal distributions.

Normal Distribution
Density Function f(x)
Distribution Function F(x)
Mean mu
Variance sigma^2
Standard Deviation sigma^2
Uniform Distribution

The uniform distribution has a constant success rate on the interval a<=x<=b and zero success rate anywhere else. The uniform distribution has the following important properties. See plots of uniform distributions.

Uniform Distribution
Density Function f(x)
Distribution Function F(x)
Mean mu
Variance sigma^2
Standard Deviation sigma^2
Exponential Distribution

The Exponential distribution arises in the calculations of reliability. It is similar to the Poisson distribution with x=0 and the probability of the desired outcome diminishes as the trial number increases (n~inf, p=0). See plots of exponential distributions.

Exponential Distribution
Density Function f(x)
Distribution Function F(x)
Mean mu
Variance sigma^2
Standard Deviation sigma^2

where lambda=const.>0.