probability distribution

A probability distribution $P$ is a function that provides the probabilities of occurrence of different possible outcomes in an experiment / of a random variable $X$ at a particular value $x$, given the parameters $\theta$.
In simpler terms, it is a model of the likelihood of an event/outcome/value, given some parameters that characterize a system:

$$X\sim P(X=x\mid \theta )$$

The sum of the probabilities in the distribution must be equal to 1:

$$\sum _{i}P(X=x_i)=1$$

Or for the continuous case:

$${\int }_{-\infty }^{\infty }f(x)dx=1$$

bernoulli distributions model binary outcomes.
binomial distributions are used to model the number of successes in a fixed number of trials.
normal distributions arise in many natural processes; as you add up many random variables, their sum tends to follow a normal distribution, (Central Limit Theorem), even if they don’t follow a normal distribution individually.
poisson distributions are used to model the number of events occurring in a fixed interval of time or space; rare events.
exponential distributions are model the probability of waiting times between poisson events.
multinomial distribution is a generalization of the binomial distribution to more than two categories.
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machine learning is essentiall learning unknown probability distributions from data.

References

normal dist statquest
goated explainer article