What does the <> enclosing the Xj in the following equation mean? Do I just treat them like ordinary parenthesis or does it mean something different? Given that the data in question is a matrix and the notation i,j is used, does this mean I divide the sum of all elements in each column by 1?

$$ Wj=\frac{1}{<Xj>}$$

To give you some context I'm following the equations on the following page for writing a fitness function for optimization (http://copasi.org/Support/User_Manual/Tasks/Parameter_Estimation/Experimental_Data/ )

Thank you

  • 1
    $\begingroup$ In this context, mean. $\endgroup$ Commented Oct 25, 2015 at 10:53
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    $\begingroup$ To physicists (and some others), $\langle Z\rangle$ is the mean/expectation $E(Z)$. $\endgroup$
    – Did
    Commented Oct 25, 2015 at 10:54

1 Answer 1


For a discrete variables:

$$<X>=\bar X=E(X)=\Sigma_{i=1}^N x_i P(x_i)$$

and for a continuous variables:

$$<X>=\bar X=E(X)=\int_{-\infty}^{+\infty} x f(x)$$

where $P$ is probability function and $f$ is probability density function

For probability domain of $\Omega$:

Discrete variables:

$$<X>=\bar X=E(X)=\Sigma_\Omega x_i P(x_i)$$

Continuous variables:

$$<X>=\bar X=E(X)=\int_\Omega x f(x)$$


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