I've been stuck on this question for a while. Two coins are selected at random from $3$ pennies, $2$ nickels, and $1$ dime with no replacement, and $X$ is the sum of the two coins. What is the probability function and the expected value?
My solution: For probability function for $X$,
$f(x)=\begin{cases} \frac36\cdot\frac25,&\text{for }X=2\text{ cents}\\\\ \frac26\cdot\frac25,&\text{for }X=6\text{ cents}\\\\ \frac36\cdot\frac15,&\text{for }X=11\text{ cents}\\\\ \frac36\cdot\frac15,&\text{for }X=10\text{ cents}\\\\ \frac16\cdot\frac35,&\text{for }X=15\text{ cents}\;. \end{cases}$
I can not seem to get a reasonable solution for $\mathrm{E}X$, because $\mathrm{E}X$ is a mean value where each value that $X$ takes on is either $2, 6, 10, 11$, or $15$ cents. I can't spend any more time on this, it's driving me nuts. Thanks!