To readers familiar with Signal and System analysis in Engineering, it will be second nature to apply the Fourier and Laplace transforms as a powerful tool for mapping functions from one domain to another in order to simplify subsequent analysis. This video looks at using this trick for mapping the probability density function (pdf) into a characteristic or moment generating function, which can then easily be used for a number of probability analysis problems. The key application here is for calculating moments for continuous random variables. The probability generating function (PGF), which is the z-transform of the pdf, is used in the same way for dealing with discrete-random variables. Finally, cumulants are also mentioned. An example of calculating the PGF for a geometric distribution is presented.