Conditional probability of second journey time given first

[bradyj7]

Hi there,

I have the journey times of 2 journeys. Would somebody be able to show me by way of example how to calculate the conditional probability function of the second journey time given the first journey time?

https://dl.dropbox.com/u/54057365/All/jt.JPG

Appreciate your help

Thanks

John

 

[haruspex]

You cannot deduce such a probability without constructing some relationship between the underlying variables. Wherever possible, this should be grounded in the knowledge of the physical system, not just abstract datapoints. In the present case, would I be right in guessing that the two times for a journey are effectively samples of the same r.v.? If so, you need to use the data to construct a family of probability distributions for these different r.v.s. E.g., they could be normally distributed with variances functionally related to their means. (But normal dist is likely not a good bet since they cannot go negative.)