In my textbook it talks about the binary indicator function. It says "The distribution represents the fact that X is always equal to the value 1, in other words, it is a constant". Is big X the state space? What is the meaning of the big X in this context?

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#### Best Answer

$X$ is a random variable that can take on values ${1,2,3,4,5}$.

An indicator variable takes on a value of $1$ if the expression inside of the indicator function is true and $0$ otherwise.

For the degenerate distribution, the indicator variable will take on a value of $1$ when $x=1$ and $0$ otherwise. We can see that for $x=1, p(X=1)=I(x=1)=1$ while for $xne 1, p(X=x)=I(x=1)=0$. In other words, the probability that the random variable takes on a value of $1$ is $1$ so $X$ always takes on a value of $1$.

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