Here are three characteristics that all probability distributions have:
The total probability is always equal to 1: This means that the probability distribution must cover all possible outcomes, and the sum of the probabilities for all possible outcomes must add up to 1. In other words, the probability distribution represents all possible events and the total probability of all those events is equal to 1.
Probabilities are non-negative: All probabilities in a probability distribution must be non-negative, meaning they can't be negative numbers. Probabilities must be greater than or equal to zero and less than or equal to one.
The probability distribution can be continuous or discrete: A probability distribution can be either continuous or discrete. A discrete probability distribution is one where the random variable can only take on certain specific values, while a continuous probability distribution is one where the random variable can take on any value within a certain range. Regardless of whether the distribution is continuous or discrete, it must satisfy the first two characteristics mentioned above.
These characteristics are fundamental to all probability distributions, and they help ensure that probability distributions are consistent and meaningful in representing real-world events and outcomes.