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Discrete
The triangular, uniform, binomial, Poisson, geometric, exponential and Gaussian distributions are some that can be so defined. In fact, the Poisson and exponential need only the mean.
Assuming that "piossion" refers to Poisson, they are simply different probability distributions that are applicable in different situations.
There are several tens of families of distributions. Some of these are: Uniform discrete Binomial Geometric Hypergeometric Poisson Random Uniform continuous Gaussian (Normal) Exponential Student's t Fisher F Chi-squared Gamma Weibull Beta Log-normal In addition, there are distributions that are associated with a particular scenario or test statistic.
Yes.