TIA Exam 4 Question 3

[Bananas88]

I tried googling this problem, and searching on here for anything with a similar issue and I'm utterly lost.

The question says
Suppose that X is a Poisson random variable with mean 2.5 and Y is a geometric random variable on 1,2... with mean 2.5. Let P denote the probability that X is equal to its mode, and let Q denote the probability that Y is equal to its mode. Find |P-Q|.

My problem is with finding Q (I got the same P as the online solution did). For a geometric series, I thought that the mean is equal to (1-p)/p, so shouldn't p be equal to 2/7? In the solution they have the mean being 1/p=1/2.5, so, since the mode is 1, they got Q as being 0.4, while I had it as 2/7.

What am I doing wrong here?

Thanks for any help!

[Gandalf]

Originally Posted by Bananas88

Y is a geometric random variable on 1,2... with mean 2.5.

There are two versions of the geometric distribution. One on {1,2,...} the other on {0,1,2,...}. They told you to use the first. You used the second.

[Gandalf]

See the thread containing this post

http://www.actuarialoutpost.com/actu...93#post4684993

or many other such threads found by searching for geometric

[Actuarialsuck]

Or a wikipedia article on geometric distribution

[Bananas88]

I didn't realize there was a difference in means for the two, thanks a ton for pointing it out/explaining, I really appreciate it!