Probability distributions

Let X be a random variable that can take on the values ​​x₁, x₂,..., x_n depending on the outcome of the experiment and let {X=x_i} be the set of all outcomes of the experiment e such that X(e) = x_i. The probability of this event P(X=x_i) is itself a function of x_i and is called the probability mass function (or probability distribution) of X, and the sum of all probabilities is equal to 1.

If X is a random variable that takes on values ​​on a discrete scale, then we speak of discrete probability distributions. Some important distributions of discrete random variables are:

• binomial,
• geometric,
• Poisson, etc.

If X is a random variable that takes values ​​on a continuous scale, then this function is called the distribution density function. Some important distribution density functions are:

• normal,
• exponential, etc.

Knowing the process that generates the shape of the distribution allows us to guess its shape.