For the binomial, it is independent trials and a constant probability of success in each trial.
For the Poisson, it is that the probability of an event occurring in an interval (time or space) being constant and independent.
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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.
Yes.
Why belong exponential family for poisson distribution
In parametric statistical analysis we always have some probability distributions such as Normal, Binomial, Poisson uniform etc.In statistics we always work with data. So Probability distribution means "from which distribution the data are?