# Exam P Practice Problem 26 – Uniform Distribution

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This post has no alternate problem. It has one problem with 3 parts.

Problem 26

For an office worker, the length of time, $X$, of the bus ride from home to office follows a uniform distribution from $0$ to $20$ minutes and the length of time, $Y$, of the bus ride from office back to home follows a uniform distribution from $0$ to $25$ minutes.

Suppose that length of bus rides in one direction is independent of the length of bus rides in the other direction.

In recent weeks, the worker finds that the total daily time spent on bus rides always exceeds $20$ minutes.

1. What is the probability that the bus ride to return home will take more than 10 minutes?
2. What is the expected length of the bus rides from office to home?
3. What is the variance of the length of the bus rides from office to home?

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