Short Quiz

Calculate standard deviation for the discrete distribution: $$\begin{array}{|c|c|c|c|c|c|} \hline x_i & 3 & 8 & 13 & 18 & 23 \\ \hline f_i & 7 & 10 & 15 & 10 & 6 \\ \hline \end{array}$$ (Given \(N = 48\))

A financial analyst defines a portfolio return \(Y = 4X + 7\), where \(X\) represents daily asset returns with a variance \(\sigma_X^2 = 5\). Calculate the variance of \(Y\) (\(\sigma_Y^2\)).

The Mean Deviation about mean for a dataset is calculated to be \(M.D.(x) = 4.50\). If every observation \(x_i\) is transformed according to \(y_i = -3x_i + 10\), calculate the new Mean Deviation \(M.D.(y)\).

A logistics center must be located along a highway at coordinate \(a\) to minimize total travel distance \(\sum_{i=1}^{5} |x_i - a|\) to five retail outlets located at coordinates \(x = 3, 7, 11, 19, 25\). Calculate the optimal location \(a\) and the resulting minimum total distance.