A fair coin is flipped $3$ times. Consider a random variable $X$ which is the number of runs. Number of runs is the number of changes of letter $H$ and $T$. For example, $HHH$ has one run, $TTH$ has two runs and $THT$ has three runs. Find the probability distribution of the random variable $X$.
My work: I don't understand the phrasing of this question. In examples in my textbook and online $X$ is defined as the number of heads or tails. But I can't follow where the example in this question is going. I would think that $TTH$ and $THT$ would both have 2 runs since $HHH$ only has one. I don't know what zero runs would be either. Can anyone give me guidance on what exactly this question means? I'm pretty sure I can solve it once I understand what the number of runs means.
The outcomes would be:
I don't know what number of $X$ would correspond with each.