0
1
Infinite
Cannot be determined
Answer is Right!
Answer is Wrong!
The correct answer is A. 0.
The self-information of a random variable $X$ is defined as $I(X;X) = -\log_2 P(X)$, where $P(X)$ is the probability of $X$ occurring. If $X$ is a constant random variable, then $P(X) = 1$ and $I(X;X) = 0$.
Option B is incorrect because $I(X;X) \neq 1$ for any random variable $X$. Option C is incorrect because $I(X;X)$ is finite for any random variable $X$. Option D is incorrect because $I(X;X)$ can be determined for any random variable $X$.