Methods2025 NHT Exam 2 Section A · Q12CAS active1 mark

Expected value of points in a die game

A game consists of rolling a fair six-sided die. Points are scored according to the following table.

| Number rolled | Points | |---|---| | 1 or 2 | 6 | | 3, 4 or 5 | $-3$ | | 6 | 9 |

Table of points scored: rolling 1 or 2 scores 6 points, rolling 3, 4 or 5 scores −3 points, and rolling 6 scores 9 points.

Let $X$ be the random variable representing the number of points scored per roll.

The mean $\operatorname{E}(X)$ is

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