1. **State the problem:** We want to find the expected value (long-term average) of the number of tasks a computer program performs each week. 2. **Recall the formula for expected value:** For a discrete random variable $X$ with possible values $x_i$ and probabilities $P(X=x_i)$, the expected value $E(X)$ is given by: $$E(X) = \sum_i x_i P(X=x_i)$$ 3. **Identify the values and probabilities:** - $x_0 = 0$ tasks with probability $P(X=0) = 0.2$ - $x_1 = 1$ task with probability $P(X=1) = 0.5$ - $x_2 = 2$ tasks with probability $P(X=2) = 0.3$ 4. **Calculate the expected value:** $$E(X) = 0 \times 0.2 + 1 \times 0.5 + 2 \times 0.3$$ $$E(X) = 0 + 0.5 + 0.6 = 1.1$$ 5. **Interpretation:** On average, the computer program performs 1.1 tasks per week over the long term.