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how i can Define correlation among more than two random variables ? how we can calculate correlation between more than two random variables?

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    You build a matrix that represents the correlation between each pair. – 2017-01-05
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    how we can build a matrix that represents the correlation between each pair? – 2017-01-05
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    There are multivariate models that involve connections amongst several variables. If you have a specific situation in mind, try explaining that instead of stating the problem so generally and abstractly. Then someone might be able to address the specific situation that matters to you. (One example is in regression of $Y$ on two predictor variables $X_1$ and $X_2$; then the $R^2$ for the regression expresses the connection between $Y$ and the $X_i$ taken together.) – 2017-01-06

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Usually, you just show one triangle of the matrix

$\begin{matrix} --\\\rho_{12} &--\\\rho_{13} & \rho_{23} &-- \end{matrix}$

The main diagonals we know are 1. (the correlation between X and itself is 1).

But there is no reason you can't build it out as a symmetric matrix.

$\begin{matrix} 1&\rho_{21} & \rho_{31}\\\rho_{12} &1&\rho_{32}\\\rho_{13} & \rho_{23} &1 \end{matrix}$

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    my question is on Corr(X,Y,Z) if X Y and Z are random variable – 2017-01-05
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    It is not defined. It is a little bit like finding the distance between 3 points. Correlations can only be compared pairwise. And if you have 3 random variables, then you have 3 pairs of correlations. – 2017-01-05