How to Solve Moments and Transformations — Univariate RV — coefficient of variation Questions on Exam P
Sample Practice Problem
ID: #ALSAV
A gamma loss has integer shape 2 and rate 0.001. Calculate its coefficient of variation.
📖 Worked Solution & Strategy
View the loss as the sum of \(2\) independent exponentials, each with mean \(1000\) and variance \(1{,}000{,}000\). Hence the gamma mean is \(2(1000)\), its variance is \(2(1{,}000{,}000)\), and \(\operatorname{CV}=\operatorname{SD}/\operatorname{E}[X]=1/\sqrt{2}\).