1. The problem is to understand the formula for the function $H(X,Y)$. 2. Typically, $H(X,Y)$ could represent a function of two variables $X$ and $Y$. Without additional context, a common example is the joint entropy in information theory, defined as: $$H(X,Y) = -\sum_{x,y} p(x,y) \log p(x,y)$$ where $p(x,y)$ is the joint probability distribution of $X$ and $Y$. 3. This formula measures the uncertainty or information content in the joint distribution of $X$ and $Y$. 4. Important rules: - The probabilities $p(x,y)$ must satisfy $0 \leq p(x,y) \leq 1$ and $\sum_{x,y} p(x,y) = 1$. - The logarithm base can be 2 (bits), $e$ (nats), or 10 (digits), depending on the context. 5. To compute $H(X,Y)$, you sum over all possible pairs $(x,y)$ the product of $-p(x,y)$ and the logarithm of $p(x,y)$. 6. This formula generalizes the entropy of a single variable to two variables, capturing their joint uncertainty.