1.2.1 Discrete and Continuous Probability Distributions


• The Binomial distribution is,



• The Poisson distribution is,



• The Hypergeometric distribution is,



• The Normal distribution is,




1.2.2 Basic Polynomials


• The quadratic equation appears in almost every engineering discipline, therefore is of great importance.



• Cubic equations also appear on a regular basic, and as a result should also be considered.



• On a few occasions a quartic equation will also have to be solved. This can be done by first reducing the equation to a quadratic,




1.2.3 Partial Fractions


• The next is a flowchart for partial fraction expansions.



• The partial fraction expansion for,



• Consider the example below where the order of the numerator is larger than the denominator.



• When the order of the denominator terms is greater than 1 it requires an expanded partial fraction form, as shown below.



• We can solve the previous problem using the algebra technique.



1.2.4 Summation and Series


• The notation is equivalent to assuming and are integers and . The index variable is a placeholder whose name does not matter.


• Operations on summations:







• Some common summations:


for both real and complex .

for both real and complex . For , the summation does not converge.