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ktau2010 · **Joined:** Thu, 14 Jun 2012 16:15:13 UTC **Posts:** 4

a bus arrives at a bus stop every 30 min. however there is no set schedule for the bus. you just know it does arrive every 30 min. you arrive at the bus stop not knowing when the last bus left. what is the probability that you will more than 15 min?

I don't understand how to do this problem. please help.

mathematic · **Joined:** Fri, 1 Jul 2011 01:17:26 UTC **Posts:** 321

ktau2010 wrote:

a bus arrives at a bus stop every 30 min. however there is no set schedule for the bus. you just know it does arrive every 30 min. you arrive at the bus stop not knowing when the last bus left. what is the probability that you will more than 15 min?

I don't understand how to do this problem. please help.

It looks like the arrival time for the next bus is uniformly distributed between 0 and 30 minutes, so the probability of waiting more than 15 minutes is 1/2.

Shadow · **Posted:** Wed, 11 Jul 2012 23:08:15 UTC

ktau2010 wrote:

a bus arrives at a bus stop every 30 min. however there is no set schedule for the bus. you just know it does arrive every 30 min. you arrive at the bus stop not knowing when the last bus left. what is the probability that you will more than 15 min?

I don't understand how to do this problem. please help.

You have wait time is a uniform random variable, so the cumulative distribution function is $P(X>x)= \begin{cases}1 & <x<0 \\ 1-{x\over 30} & 0\le x\le 30 \\ 0 & 30<x\end{cases}$ .

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