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

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