Mean and Variance of X with possible outcomes I roll a six-sided die until I get a 6. Then I roll it some more until I get an
even number. Let X be the total number of rolls. So here are some possible
outcomes with the resulting value of X:
24 1 2 6 1 5 4 : X = 8
3 6 4 : X = 3
3 4 6 3 1 1 2 : X = 7
1 5 4 6 6 : X = 5
Find the mean and variance of X.
I believe the best way to approach this is to write X as the sum of two (or more) random variables. But I am just a little confused on where to begin.

Expressing $X$ as a sum of two simple random variables is indeed the best approach.
Let $U$ be the number of tosses until we get a $6$, and $V$ the number of additional tosses until we get an even number. Then $X=U+V$. 
Note that $U$ and $V$ each have geometric distribution (with different parameters), and are independent.
The mean of $X$ is the sum of the means of $U$ and of $V$, and (by independence) the variance of $X$ is the sum of the variances of $U$ and $V$.
