Simulation in R

Normal Distribution:

Poisson Distribution:

Quantile function in Wiki: In probability and statistics, the quantile function specifies, for a given probability in the probability distribution of a random variable, the value at which the probability of the random variable will be less than or equal to that probability. It is also called the percent point function or inverse cumulative distribution function. The quantile function is one way of prescribing a probability distribution, and it is an alternative to the probability density function (pdf) or probability mass function, the cumulative distribution function(cdf) and the characteristic function. The quantile function, Q, of a probability distribution is the inverse of its cumulative distribution function F. The derivative of the quantile function, namely the quantile density function, is yet another way of prescribing a probability distribution. It is the reciprocal of the pdf composed with the quantile function.