A random variable is a variable whose value is unknown, or a variable for which the value changes over different iterations of the experiment.
For example, when we roll a die, the outcome of rolling the dice will vary over different iterations and hence the outcome becomes a random variable.
A random variable is discrete if the outcome of the random variable is limited to a few possible outcomes.
For example, the outcome of rolling a fair dice can only be 1, 2, 3, 4, 5, or 6; it cannot be a number beyond that. Thus, the outcome is limited to only a few possible values.
In the previous example, whenever a die is rolled, there is a probability associated with each outcome. For example, if a fair dice is rolled once, the probability that the outcome is 4 is 1/6, as all outcomes have an equal chance of being obtained...