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!