The characteristic feature in all the discrete distributions is that the random variable X is discrete. The possible outcomes are distinct numbers, which is why we called them discrete probability distributions.
Have you asked yourself, “what if the random variable X is continuous?” What is the probability that X can take any particular value x on the real number line which has infinite possibilities?
For a continuous random variable, the number of possible outcomes is infinite, hence,
P(X = x) = 0.
For continuous random variables, the probability is defined in an interval between two values. It is computed using continuous probability distribution functions.
Learn more about these fundamentals in Lesson 41.
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