I am looking for some insight into a problem:
Consider a group of $T$ persons, and let $a_1, a_2, ..., a_T$ denote the height of these $T$ persons. Suppose that $n$ are selected from this group at random without replacement, and let $X$ denote the sum of the heights of these $n$ persons. I'm supposed to find the mean and the variance.
This is in the section of hypergeometric distributions for my probability textbook, so I am trying to see how to turn this into an "urn" problem. Normally, I think one would split $X = X_1+...+X_T$ where $X_i = 1$ is chosen, $0$ otherwise, where the probability in this problem would be $Pr(X_i = 1) = \frac{1}{T}$, but I am confused because each $X_i$ is "weighted" by the height. I was having trouble finding other useful examples online.
EDIT: Here is how the book explains hypergeometric distributions:
Assume that $n$ balls are selected at random without replacement from a box containing $A$ red balls and $B$ blue balls. The expected number of red balls is $E(X) = \frac{nA}{A+B}$ and the variance is $Var(X) = \frac{nAB}{(A+B)^2}\cdot\frac{A+B-n}{A+B-1}$
I am trying to understand how to use these formulas for this particular problem. I am pretty sure I can calculate each straight from the definitions.