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j2005
May 20th 2006, 06:45 AM
Anyone know how to solve this problem?--You and your co-worker arrive at train station where the number of train follow the possion process at 20 per hour, 25% are express and 75% are local. local gets you to work in 28 minutes and express in 16 minutes. you arrrive at station at 7:01am, your co-worker at 7:02am, there is a local train arrive at 7:03am. what is difference between expected time you and your co-worker get to work?
Thanks a lot!

PhillyP
May 21st 2006, 10:31 AM
The expected time should be the same I beleive. The 7:01 and 7:02 is irrelevant since the time between trains follows exponential (memoryless). You would get on your local train and arrive in 28 minutes...Your coworker would would wait a mean time of 12 minutes for their train to arrive (poisson with mean of 5 per 60 minutes which is the same as Poisson with mean of 1 per 12 minutes...i.e. 12 minutes mean wait time.) and then it takes their train 16 minutes to arrive once they are on board...so they end up taking 28 minutes as well.

j2005
May 22nd 2006, 06:32 AM
I thought it's the same first, then I changed my mind.

bv12
May 23rd 2006, 03:22 PM
I like those problems; they are almost gimmes. Too bad there was 1 and not 3 or 4 on the exam. The Markov Chain questions come easy to me too.