Follow up questions: a) What is the expected value of the sum of the rolls b) What is the expected value of the product of the rolls c) What is the variance of the sum of the rolls
2026-03-29 03:36:39.1774755399
Suppose you roll three fair six-sided dice. Compute the expected value of the product of rolls.
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Hint
If we denote the outcome of the $i$-th die by $X_i$, we desire to calculate$$E\{X_1X_2X_3\}=E\{X_1\}E\{X_2\}E\{X_3\}$$and$$E\{(X_1+X_2+X_3)^2\}-E^2\{X_1+X_2+X_3\}$$ Simply use the statistical independence of the $X_i$s, which yields to $$E\{X_iX_j\}=E\{X_i\}E\{X_j\}\quad,\quad i\ne j$$