The Laplace transform and the moment generating function method. (omg.) how using e^x (and expectation or improper integration) is able to simplify analysis and computation.
And how the mgf method is useful to describe ubiquitous statistical distribution like normal and gamma.
Like normal distribution, the ubiquity of the Gamma distribution. (omg.) how Gamma is a generalisation of the exponential and chi square distribution. how the sum of i.i.d gamma distribution still follows gamma distribution. etc.