2.2 FUNCTIONS

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2.2.1 Discrete and Continuous Probability Distributions

The Binomial distribution is,

The Poisson distribution is,

The Hypergeometric distribution is,

The Normal distribution is,

2.2.2 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,

2.2.3 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.

2.2.4 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.