Probability: joint probability distribution problem?

1. Apr 8, 2010

libelec

1. The problem statement, all variables and given/known data
John and George are set to meet each other at 12 o'clock. John's time of arrival, J, is distributed uniformly between 12:00 and 12:15. John will wait for George for 15 minutes. If he doesn't show up, he leaves. George's time of arrival, G, is also uniformly distributed, between 12:05 and 12:20. But he will only wait 5 minutes for John.

Find the probability of an encounter.

3. The attempt at a solution

I'm at complete lost with this problem. I think that what I have to do is find the jount probability distribution of J and G, but I couldn't say why. And the "waits for 15 minutes" thing also confuses me.

Any ideas?

2. Apr 8, 2010

Anybody?

3. Apr 8, 2010

vela

Staff Emeritus
Hint: Let T=G-J. For what range of values of T will an encounter happen?

4. Apr 8, 2010

libelec

T between 0:00 and 0:05...

OK, and I have to do the same thing but considering T2 = J-G. How can I then find the entire answer? T+T2?

5. Apr 8, 2010

vela

Staff Emeritus
Note that T2 = -T, so it's essentially the same variable. In other words, if you have something like a<T2<b, that's the same as -a>T>-b. You only have to work with one variable. There's no need to work the cases out separately and combine them at the end.

6. Apr 10, 2010

libelec

No, no, I see. T has to be between -0:15 and 0:05, right? Because if G<J, T<0, and since J can only be 15 minutes earlier than G otherwise he leaves, T> -0:15. and if G>J, T>0, and since G can only be 5 minutes earlier than J, T<0:05.

So, what I'm looking for is P(-0:15<= T <= 0:05), right?

7. Apr 10, 2010

vela

Staff Emeritus
Right!

8. Apr 11, 2010

libelec

OK, thanks.

9. Sep 13, 2010

cgchayan

All understood.. but how to find out the p.d.f of T? Because without the pdf of T the required probability cannot be calculated..