Median of three uniforms on zero to four above 3

Question

Draw three independent values from the uniform distribution on $[0,4]$ . Find the probability that their median exceeds 3.

Short answer

$5/32$ . The median exceeds 3 when at least two values do, each with probability $\tfrac14$ : $3\cdot\left(\tfrac14\right)^2\tfrac34+\left(\tfrac14\right)^3=\tfrac{9}{64}+\tfrac{1}{64}=\tfrac{10}{64}$ .

Adapted from OpenQuant; question and answer rewritten by SelfMadeQuant.com.

See the hint and the full worked solution in the question bank (free account).

Open the worked solution

Lessons behind this question

Continuous Random Variables and Probability Density Functions
Independence
Cumulative Distribution Functions

Start with a free lesson: Normal Distribution is part of a free topic. Create a free account, no card needed, to read it in full with worked solutions.

Read it free