Hi folks. My class (not a probability course) just covered a bunch of probability in one class period. Last prob course I had was in early high school so I'm a little fuzzy on it.

Here's an example we have to work on:

Everyone goes to a party with a gift and gives it to the secret santa, who passes them back to everyone randomly (in a random order). If n people go to the party, what is the expected number of party-goers that will get their own gifts back?

I need to use Indicator Random Variables for this. So here's what I have.

So each person either gets the gift or does not.

SO, first thing's first, I need to identify my IRV C_i

Next, since C is the random variable that represents # of people who got back their own gifts...

Then, getting a good gift back is:

And getting your own gift back is:

So our expected value of C_i is:

And finally, the expected value of C is...

(I hope you like my latex, I really tried to learn that for this post. )

So is this right? Any advice? Thanks!