1. The problem is to find the expected value $E(X)$ and the variance $\mathrm{Var}(X)$ of a random variable $X$ given its probability distribution. 2. The expected value formula is: $$E(X) = \sum x P(x)$$ where $x$ are the values of the random variable and $P(x)$ are their probabilities. 3. From the problem, we have: $$E(X) = \frac{1}{6}(20 + 40 - 30) = \frac{1}{6} \times 30 = 5$$ 4. The variance formula is: $$\mathrm{Var}(X) = E(X^2) - [E(X)]^2$$ where $E(X^2)$ is the expected value of the square of $X$. 5. To find $\mathrm{Var}(X)$, we need $E(X^2)$, which is not given here, so we cannot compute the variance without additional information. 6. Summary: - Expected value $E(X) = 5$ - Variance $\mathrm{Var}(X)$ cannot be computed without $E(X^2)$