Probability Distribution of Discrete Random Variable

Once a discrete random variable has been defined on a sample space, the natural next step is to ask: how likely is each of its possible values? Consider rolling two dice and letting $X$ be the sum of the numbers shown — $X$ can take any of the values $2, 3, 4, \dots, 12$, each with its own likelihood based on how many outcomes in the sample space produce that sum.

Listing every possible value of $X$ alongside the probability of it occurring gives a probability distribution table for that random variable. Such a table links every possible outcome of the random experiment to the probability of the corresponding event, and together the listed values account for the entire sample space.