The basics of discrete probability distributions

Let’s start with the fundamentals. What is a random variable? A random variable is a set of possible outcomes from a random experiment. For example, if we want to know whether tomorrow’s weather is sunny or rainy, then “tomorrow’s weather” is the random variable, and the possible outcomes are “sunny” and “rainy.” A random variable can be discrete or continuous. If a random variable takes only a finite number of distinct values such as “sunny” or “rainy,” it is a discrete random variable. If a random variable can have a continuum of infinite and uncountable outcomes, it is a continuous random variable. Then, a discrete probability distribution is a distribution that shows all possible discrete values with respective probabilities for each value. When we say tomorrow is 70% sunny and 30% rainy, we are saying the random x variable has two outcomes...