A constant has only one unvarying value under all circumstances for example p=pie
and c = speed of light. Few things are constant in the universe. Most phenomena exhibit variation. To humans this variation
is random because of ignorance of the under-lying deterministic order. A random variable is one whose value changes. It can
be quantitative (with intrinsic numerical value) or qualitative (descriptive with no intrinsic numerical value).

QUANTITATIVE
RANDOM VARIABLES

A
random quantitative variable results when numerical values are assigned to results of measurement or counting. It is called
a discrete random variable if the assignment is based on counting. It is called a continuous random variable if the numerical
assignment is based on measurement.

The
numerical continuous random variable can be expressed as fractions and decimals. The numerical discrete random variable can
only be expressed as whole numbers.

Choice
of the technique of statistical analysis depends on the type of variable. Each type of random variable corresponds to a statistical
distribution used in statistical analysis. This relation is too advanced to be discussed in more detail in this elementary
course.

QUALITATIVE
RANDOM VARIABLES

Qualitative variables (nominal, ordinal, and ranked) are attribute or categorical with
no intrinsic numerical value. The nominal has no ordering for example male or female. The ordinal has ordering for example
first class, second class, third class. The ranked has observations arrayed in ascending or descending orders of magnitude
for example 1^{st}, 2^{nd}, 3rd.

RANDOM VARIABLES:
PROPERTIES

A random variable has 6 properties. The **expectation** or
average of a random variable is a central value around which it hovers most of the time. The variations of the random variable
around the average are measured by its **variance**. **Covariance** measures the co-variability of the two random variables. **Correlation**
measures the linear relation between two random variables. **Skew ness** measures
the bias of the distribution of the random variable from the center. **Kurtosis**
measures the peaked ness of the random variable is at the point of its expectation.

RANDOM VARIABLES: MATHEMATICAL TRANSFORMATIONS

Quantitative variables can be transformed into qualitative ones. Qualitative variables can be transformed
into quantitative ones but this is less desirable. The continuous variable can be transformed into the discrete variable.
Transformation of the discrete into the continuous may be misleading.

**Discussion**

- Determine the type of each variable in the class data
- Determine the type of each variable in a clinical laboratory report