I have a random variable $X$ which is distributed uniformly over $[0,b]$. I want to know based on only one observation what is the confidence level of the interval $[X, 4X]$? I know this entails finding $P(X \leq b \leq 4X)$ but am entirely unsure how to approach the question. I have only had experience constructing confidence intervals for normally distributed variable and am very thrown off by the fact that $X$ is distributed uniformly.


It's always the case that $X \leq b$, so you only need to find

\begin{align} P(b \leq 4X) &= P(1/4 \leq X / b) \\ &= 1 - P(X / b < 1/4) \\ &= 1 - 1/4 \\ &= 3/4 \end{align}

since $X / b \sim$ uniform$[0, 1]$.

| cite | improve this answer | |

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.