Question

You arrive at the train station between 7:20 am and 7:30 am, uniformly. The train arrives every 8 minutes starting from 7:00 am. Let Y be the waiting time. Please compute the pdf of Y.

Answer 1

You arrive at train station between 7.20am and 7.30 am,uniformly

that is 7.20am , 7.21am, 7.22am,7.23am, 7.24am , 7.25am , 7.26am , 7.27am , 7.28am , 7.29am , 7.30am

Train arrives after every 8min starting from 7.00am

that is   7.00am , 7.08am , 7.16am , 7.24am , 7.32am, 7.40am respectively

So waiting time Y if a person is arriving between 7.20am and 7.24am and train arriving at 7.24am will be the difference between the two

that is 7.24am - (7.20,7.21,7.22,7.23,7.24)am that gives 4min,3min,2min,1min,0min respectively.

So waiting time Y if a person is arriving between 7.25am and 7.30am and train arriving at 7.32am will be the difference between the two

that is 7.32am - (7.25,7.26,7.27,7.28,7.29,7.30)am that gives 7min,6min,5min,4min,3min,2min respectively.

So these compute Y that is the waiting time.