Let $\pi _{1},\ldots,\pi _{k}$ be k independent normal populations with means $\mu _{1},\ldots,\mu _{k}$ and variances $\sigma _{1}^{2},\ldots,\sigma _{k}^{2 ...

For $A \subset X = \{x_1, ..., x_n \left\vert x_i \geq 0, i = 1, 2, ..., n}$, let $a_A$ and gA denote the arithmetic mean and geometric mean of elements of A ...