How to Solve Continuous Random Variables — Univariate RV — percentiles from a density Questions on Exam P
Sample Practice Problem
ID: #F3SHC
\(X\) is uniform on \((1,b)\), where \(b>1\), and \(\operatorname{E}[X]=3\operatorname{Var}(X)\). Calculate the upper endpoint \(b\).
📖 Worked Solution & Strategy
For \(X\sim\operatorname{Uniform}(1,b)\), \(\operatorname{E}[X]=(1+b)/2\) and \(\operatorname{Var}(X)=(b-1)^2/12\). Substitution into the stated moment relation gives \(3(b-1)^2=6(b+1)\). The root satisfying \(b>1\) is \(b=4.2361\). Therefore the upper endpoint is \(b=4.2361\). The evaluated result is \(4.2361\), which matches the correct option. After simplifying the displayed expression, the resulting value is \(4.2361\). This is the numerical value of the upper endpoint \(b\).