(See Steps) The correlation matrix of the random variables Y_1,Y_2,... ,Y_n is
Question: The correlation matrix of the random variables \[{{Y}_{1}},{{Y}_{2}},\ldots ,{{Y}_{n}}\] is
\[\left( \begin{matrix} 1 & \rho & \cdots & \rho \\ \rho & 1 & \cdots & \rho \\ \vdots & \vdots & \cdots & \rho \\ \rho & \rho & \cdots & 1 \\ \end{matrix} \right)\] . That is, each entry on the diagonal is 1, and each off-diagonal entry is \[\rho \] . Each random variable has variance \[{{\sigma }^{2}}\] . Find the variance of \[{{\bar{Y}}_{n}}\] .
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