# Average passanger waiting time - probability density function - normal distribution

Hello guys, so we got this additional task to solve for a post-modul at university:

- The intermediate arrival time of a bus is normal distributed

- The expected value of the intermediate arrival time during rush hour is 4 minutes

- The standard deviation of the intermediate arrival time is 50 sec (50/60min)

A passanger enters the bus stop at a random time (statistically evenly distributed).

- What will be his waiting time for the next bus. How does the distribution (probability density function) for the passangers waiting time look like?
- What is the expected average waiting time of the passanger?
- Define the standard deviation of the passangers waiting time?
- Define the probability that the passanger has to wait more than 5 Minutes during rush hour?

I now how to solve it with a fixed arrival time of 4 minutes and how to get the standard deviation for that, but not how to solve it with a normal distribution and how to bring in the standard deviation. Our professor mentioned something about forward recurrence time, but I couldn't find anything about that. Hope someone can help me out here.

Edit: An R Code would be fine too.

Patman

7

## Answer

**Answers can be viewed only if**

- The questioner was satisfied and accepted the answer, or
- The answer was disputed, but the judge evaluated it as 100% correct.

Dynkin

779

The answer is accepted.

Join Matchmaticians Affiliate Marketing
Program to earn up to 50% commission on every question your affiliated users ask or answer.

- answered
- 463 views
- $10.05

### Related Questions

- The derivation of the formula for variance for a Pareto Distribution
- Stochastic Analysis question
- Please check if my answers are correct - statistic, probability
- Calculating P values from data.
- Correlation of Normal Random Variables
- Product of Numbers from a Log Normal Distribution
- Figuring out the maths for the probability of two adopted teens randomly being matched as pen pals in 2003
- Joint PDF evaluated over a curve $P_{U,V}$