?

Show that if p (X,Y) = 1, then p (X, X+Y) = 1.

(Note: This is a correlation problem).  I get the theory behind this but I'm not really sure how to show it mathematically.  Thanks for your help!

If we assume Var(x) is not = 0, show that p(Y, 7Y+3) = 1.  

To solve this question it is my understanding that we use the correlation formula,

 ρ(X, Y ) = Cov(X, Y) / sqrt[Var(X)] sqrt[Var(Y)].

The theory behind it makes sense but I can't figure out how to show the work here.  Thanks for your help!

An interviewer is given a list of potential people she can interview. She needs five interviews to complete her assignment. Suppose that each person agrees independently to be interviewed with probability 2/3. What

is the probability she can complete her assignment if the list has 8 names?

I'm stuck on this problem because there is a chance that the interviewer will finish the interviews before getting to 8 names.  Anyone know how to solve this?