Why is it that the joint p.d.f of D and V is same as the p.d.f of V alone?

[Kunjesh Parikh]

in a two state markov model, the joint p.d,f of the statistics D and V looks exactly similar to the p.d.f of V alone with the only exception that the conditions are a bit different, but even their interpretations are same.

 

[Mark Mitchell]

Well, they're telling you about the same thing - how likely it is that a life remains under observation for a given time - so they should be very similar The joint pdf (using di to give the conditions), enables us to write the pdf in one function as shown on page 11 of Ch4, as the di effectively works like an indicator function for us.

 

[Kunjesh Parikh]

Well, they're telling you about the same thing - how likely it is that a life remains under observation for a given time - so they should be very similar The joint pdf (using di to give the conditions), enables us to write the pdf in one function as shown on page 11 of Ch4, as the di effectively works like an indicator function for us.

Ok. But, it's not really behaving like a joint p.d.f actually, instead like a marginal p.d.f only. If it was a joint p.d.f, then we should be able to get at the expected values of each of the random variables directly from it. But, i tried it and nothing came out of it.