1. **State the problem:** We are given a random variable $X$ with values $x_i = -3, 0, 4$ and corresponding probabilities $p_i = 0.4, 0.4, 0.2$. We need to find the expected value $E(X)$. 2. **Formula for expected value:** The expected value of a discrete random variable is given by $$E(X) = \sum_i x_i p_i$$ where $x_i$ are the values and $p_i$ are their probabilities. 3. **Calculate each term:** $$-3 \times 0.4 = -1.2$$ $$0 \times 0.4 = 0$$ $$4 \times 0.2 = 0.8$$ 4. **Sum the terms:** $$E(X) = -1.2 + 0 + 0.8 = -0.4$$ 5. **Interpretation:** The expected value $E(X)$ is $-0.4$, which means on average, the value of $X$ is $-0.4$. **Final answer:** $$E(X) = -0.4$$