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Statistical Mechanics

Binomial Distributions

Poisson distributions

Gaussian distribution

Distribution Characterization

Distribution Characterization

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There are a number of parameters that can be calculated with a probability distribution such as mean values and standard deviation for both discrete and continuous distributions.

ID:(310, 0)

Distribution Characterization

Description

There are a number of parameters that can be calculated with a probability distribution such as mean values and standard deviation for both discrete and continuous distributions.

Variables

Symbol

Text

Variable

Value

Units

Calculate

MKS Value

MKS Units

Calculations

Equation

Number

First, select the equation:

to

, then, select the variable:

to

Symbol

Equation

Solved

Translated

Calculations

Symbol

Equation

Solved

Translated

Variable

Given

Calculate

Target :

Equation

To be used

Equations

$ \bar{u} =\displaystyle\sum_{ i =1}^ M P(u_i) u_i $

u =sum( P(u_i) * u_i , i ,1, M )

(ID 3362)

$ \overline{f} =\displaystyle\sum_{ i =1}^ M P(u_i) f(u_i) $

f = sum( P(u_i) * f(u_i) , i , 0 , M )

(ID 3363)

$\overline{f+g}=\overline{f}+\overline{g}$

\overline{f+g}=\overline{f}+\overline{g}

(ID 3364)

$\overline{cf}=c\overline{f}$

\overline{cf}=c\overline{f}

(ID 3365)

$\overline{(\Delta u)^2}=\displaystyle\sum_{i=1}^M P(u_i)(u_i-\bar{u})^2$

\overline{(\Delta u)^2}=\sum_{i=1}^M P(u_i)(u_i-\bar{u})^2

(ID 3366)

$ \bar{u} =\displaystyle\int du\,P(u)\,u $

u =int( P(u) * u , u ,0, infty )

(ID 11432)

$ \overline{f} =\displaystyle\int P(u) f(u) du$

fu =int( P(u) * f(u) , u ,0,infty)

(ID 11433)

$ \displaystyle\sum_{ i =1}^ M P(u_i) = 1$

@SUM( P(u_i) , i ,1, M ) = 1

(ID 11434)

$ \displaystyle\int P(u) du = 1$

int( P(u) , u ,0,infty) = 1

(ID 11435)

$ \overline{(\Delta u)^2} =\displaystyle\int P(u) ( u - \bar{u} )^2 du$

mDu ^2=@INT( P(u) * ( u - mu )^2 , u )

(ID 11436)

Examples

ID:(310, 0)