Conditional probability question

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This discussion centers on calculating the conditional probability function of journey times based on provided data. John seeks guidance on how to derive this probability given two journey times. A key insight is that one cannot determine conditional probabilities without establishing a relationship between the underlying variables. It is suggested that the journey times may represent samples of the same random variable, necessitating the construction of probability distributions, potentially using normal distributions with variances related to their means.

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bradyj7
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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
 
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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.)
 

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