I am playing a dice (6-face) game where I roll 5 times and for each $i$th roll, $i = 1, 2, ..., 5$, I get $1$ point if the number I rolled is strictly larger than $i$. How do I find the expected value of the total points I earned from this game?
2026-03-28 12:32:10.1774701130
What is the expected value of points earned in a dice game with 5 rolls?
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Let $X_i$ be a random variable for the number of points earned from the $i$th roll. By linearity of expectation, the expected total points earned is $$\sum_{i=1}^5 \mathbb{E}[X_i].$$
It remains to calculate $\mathbb{E}[X_i]$, the expected number of points earned from the $i$th roll, which I will leave to you.