How to Solve Moments and Transformations — Univariate RV — moments of aX + b Questions on Exam P
Sample Practice Problem
ID: #OZJ93
A laboratory's annual consumable cost has variance 240. All prices rise by 10%, so the new cost is \((1+0.10)X\). Calculate the new variance.
📖 Worked Solution & Strategy
Let \(X\) be original cost with \(\operatorname{Var}(X) = 240\). Inflated cost is \(Y = (1 + 0.10)X = \frac{11}{10}X\). For constant scaling, \(\operatorname{Var}(cX) = c^2 \operatorname{Var}(X)\). Thus new variance is \(\operatorname{Var}(Y) = (\frac{11}{10})^2(240) = \frac{1452}{5}\). The new variance is \(\operatorname{Var}(Y) = \frac{1452}{5}\). The evaluated result is \(\frac{1452}{5}\), which matches the correct option.