Question: The correlation matrix of the random variables \[{{Y}_{1}},{{Y}_{2}},{{Y}_{3}},{{Y}_{4}}\] is \[\left( \begin{matrix} 1 & \rho & {{\rho }^{2}} & {{\rho }^{3}} \\ \rho & 1 & \rho & {{\rho }^{2}} \\ {{\rho }^{2}} & \rho & 1 & \rho \\ {{\rho }^{3}} & {{\rho }^{2}} & \rho & 1 \\ \end{matrix} \right)\] , \[0<\rho <1\] , and each random variable has variance \[{{\sigma }^{2}}\] . Find the variance of \[{{\bar{Y}}_{4}}\] .

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