How to solve Continuous Random Variables — Univariate RV — percentiles from a density questions on Exam P?

Question

$X$ is uniform on $(1,b)$, where $b>1$, and $\operatorname{E}[X]=3\operatorname{Var}(X)$. Calculate the upper endpoint $b$.

Accepted Answer

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 $b=4.2361$.

Therefore, the result is $4.2361$, so the correct answer is option (E).

How to Solve Continuous Random Variables — Univariate RV — percentiles from a density Questions on Exam P

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