This was a group presentation assignment for CSUEB STAT 620 Probability and Statistics Theory. Our objective was to derive the moment generating function (MGF) of the binomial distribution and then to use it to find the equations for the mean and variance of the distribution. The mean, which is the first central moment, is found by setting the first derivative of the MGF to zero. The variance is found by calculating the second derivative of the MGF, which is the second raw moment, setting it to zero and subtracting the squared mean to arrive at the second central moment which is the variance equation.