\problemdata
{s01 ps10}
{random variable]

\begin{problem}
\begin{problemparts}

\problempart
Suppose that I roll a 4-sided die, a 6-sided
die, an 8-sided die, a 10-sided die, a 12-sided die, and a 20-sided
die.  What is the expected number of 6's that come up?  (Assume that
all of the dice are fair.)

\problempart
Suppose that I roll $n$ dice that are
6-sided, fair, and mutually independent.  What is the expected value
of the largest number that comes up?

\hint You may want to use the ``alternative" formula for expectation:
$\expect{M} = \sum_{i=0}^{\infty} \Pr(M > i)$. (This formula is valid
since the random variables involved are non-negative.)

\end{problemparts}
\end{problem}