1. The problem is to understand and use the formula for variance, which is given by $$\sigma^2 = \sum \left[(x - \mu)^2 \cdot p(x)\right]$$ where $\sigma^2$ is the variance, $x$ represents each value, $\mu$ is the mean (expected value), and $p(x)$ is the probability of $x$. 2. This formula calculates the variance by summing the squared differences between each value and the mean, weighted by their probabilities. 3. To use this formula, first find the mean $\mu = \sum x \cdot p(x)$. 4. Then, for each value $x$, compute the squared difference $(x - \mu)^2$. 5. Multiply each squared difference by its probability $p(x)$. 6. Finally, sum all these products to get the variance $\sigma^2$. This formula is fundamental in statistics to measure how spread out values are around the mean.