

DistributionThe Engineer posted on October 23, 2006 
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Mean Value: denoted by µ, is the likely average outcome from a random sampling process.

Discrete System

Continuous



Variance: denoted by s^{2}, indicates the spread of the distribution measured from the likely outcome m.

Discrete System

Continuous



Standard Deviation: denoted by s, is the positive square root of the variance. It combines the spread of a distribution.

Discrete System

Continuous



Continuous Normal Distribution, also know as the Gaussian distribution, is the bestknown and most widely used probability distribution.

Density Function
Distribution Function

Mean = µ
Variance = s^{2}
Standard Deviation = s

Exponential Distribution, also known as the negative exponential, is useful in the calculations of reliability. The probability of the desired outcome diminishes as the trial number increases.

Density Function 
Distribution Function 


Mean = µ
Variance = s^{2}
Standard Deviation = s

Discrete Binomial Distribution, also known as Bernoulli distribution. If the probability of occurrence of an event in each trial is p, and the probability of nonoccurrence is 1p, then the probability of exactly x occurrence among n trial has the following properties:

Density Function 
Distribution Function 


Mean = µ
Variance = s^{2}
Standard Deviation = s

Poisson Distribution is useful to describe the desired outcomes occur infrequently but at a regular rate. If the mean occurrence rate is V (the average of occurrence of the event) and the event took place during a time interval t, the poisson distribution with exactly x successes in the same sampling period has the following properties.

Density Function 
Distribution Function 



Mean = µ
Variance = s^{2}
Standard Deviation = s 