First i will explain the binomial expansion
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Poisson and Binomial both the distribution are used for defining discrete events.You can tell that Poisson distribution is a subset of Binomial distribution. Binomial is the most preliminary distribution to encounter probability and statistical problems. On the other hand when any event occurs with a fixed time interval and having a fixed average rate then it is Poisson distribution.
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If X and Y are independent Gaussian random variables with mean 0 and standard deviation sigma, then sqrt(X^2 + Y^2) has a Rayleigh distribution with parameter sigma.
A simple continuous distribution can take any value between two other values whereas a discrete distribution cannot.
The standard normal distribution is a normal distribution with mean 0 and variance 1.