I'm in a university-level probability course and I'm stuck on a homework problem. Currently we are working on multivarate probability distributions.(adsbygoogle = window.adsbygoogle || []).push({});

I have this problem:

In an earlier exercise, we considered two individuals who each tossed a coin until the first head appeared. Let Y1 and Y2 denote the number of times that persons A and B toss the coin, respectively. If heads occurs with probability p and tails occurs with probability q=1-p, it is reasonable to conclude that Y1 and Y2 are independent and that each has a geometric distribution with parameter p. Consider Y1-Y2, the difference in the number of tosses required by the two individuals.

I need to find a lot of information about the experiment, like E(Y1), E(Y2), E(Y1-Y2), etc. I think I can determine all of the other information if I can just find what E(Y1) and E(Y2) are. This problem is different from all the others we've done since it does not give the joint probability density function. Thus, I have no idea where to start. What is the joint probability density function and what are E(Y1) and E(Y2)?

I would guess that E(Y1) and E(Y2) simply equal (1/p) [from geometric distribution], but these seem horribly wrong.

Any help would be greatly appreciated.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Some Help on Probability

**Physics Forums | Science Articles, Homework Help, Discussion**