Expected ferry time with random delays

Question

A boat trip between two islands takes $12$ minutes if nothing slows it down. Along the way there are five checkpoints. Four of them each delay the boat by $1$ minute with probability $25\%$ ; the fifth delays it by $4$ minutes with probability $75\%$ . What is the expected total length of the trip in minutes?

Short answer

$16$ minutes. By linearity of expectation, add the mean delays to the base time: $12+4(0.25\times1)+0.75\times4=12+1+3=16$ .

Adapted from QuantQuestions.io; 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

Duration and Convexity: Measuring and Managing Interest Rate Sensitivity
Expectation, Mean, and Variance
Conditional Expectation and Variance Revisited

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

Read it free