# of sophomore girls? Taylor expansion? ...

**1. In a class, there are 4 freshman boys, 6 freshman girls and 6 sophomore boys.**

How many sophomore girls must be present if sex and class are to be independent when a student is selected at random?

I don't really understand this question. No sophomore girls are given in the information?

**2. Let X be a Poisson random variable with parameter λ.**

Show that P{ X is even } = 1/2 [1 + e^-2λ]. Use Taylor expansion of e^-λ + e^λ.

I set it up as

P{X is even} = e^λ [summation λ^2n / (2n)!]

how do i expand the summation part?

**3. If X is a geometric random variable, show analytically that**

P{ X = n + k | X > n } = P{X = k}.

Give a verbal argument using the intepretation of a geometric random variable as to why the above is true.

==>I simplified and got P{ X = n + k | X > n } = p(1-p)^k-1

What I don't understand is how do I give a verbal argument?

Thanks for the help in advance. Finals are coming up in 2 weeks. My prof decided to give us tons of extra discussion questions to do. These are the some of the questions I didn't understand. As for the rest, I'm still trying to do them.. please kindly help because I'm afraid that such questions will come up in the finals. If so, I'll be deadmeat coz I have no idea how to go about them.