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1.2 FUNCTIONS

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1.2.1 Discrete and Continuous Probability Distributions

• The Binomial distribution is,

• The Poisson distribution is,

• The Hypergeometric distribution is,

• The Normal distribution is,

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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,

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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.

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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.