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Consider fair $k$-sided dice with the numbers $1$ through $k$ on their faces.
a. Roll one die. Let the RV $X$ be the number on one die. Compute $E[X]$ and $V[X]$.
b. Roll $n$ dice. Let the RV $Y$ be the sum of numbers on the dice. Compute $E[Y]$.
c. Roll two dice and let the random variable $Z$ be the second die subtracted from the first. What is $E[Z]$?

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up vote 1 down vote accepted

Hints: For (a), do you know formulas for $\sum_{i=1}^k i$ and $\sum_{i=1}^k i^2$?

For (b) and (c), use the linearity property of expected value: for any random variables $X$ and $Y$ whose expected values exist and any constants $a$ and $b$, $E[aX + bY] = a E[X] + b E[Y]$.

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Thanks for the hints, I was able to solve the problems from there. – jamesio Nov 17 '11 at 6:00

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