The correct answer is B.
The mutual information between two random variables $X$ and $Y$ is defined as:
$$I(X;Y) = \sum_{x,y} p(x,y) \log \frac{p(x,y)}{p(x)p(y)}$$
where $p(x,y)$ is the joint probability distribution of $X$ and $Y$, and $p(x)$ and $p(y)$ are the marginal probability distributions of $X$ and $Y$, respectively.
If $X$ and $Y$ are statistically independent, then $p(x,y) = p(x)p(y)$ for all $x$ and $y$. Substituting this into the definition of mutual information, we get:
$$I(X;Y) = \sum_{x,y} p(x)p(y) \log \frac{p(x,y)}{p(x)p(y)} = \sum_{x,y} p(x)p(y) \log 1 = 0$$
Therefore, when $X$ and $Y$ are statistically independent, the mutual information between them is 0.
Option A is incorrect because it is the value of mutual information when $X$ and $Y$ are perfectly correlated. Option C is incorrect because it is the value of mutual information when $X$ and $Y$ are perfectly dependent but not perfectly correlated. Option D is incorrect because it is not possible to determine the value of mutual information without knowing the joint probability distribution of $X$ and $Y$.
