Discrete Random Variables

It should be known that discrete numbers in mathematics and statistics are not ones that know how to sneak around. Instead, they are countable numbers, even countably infinite numbers. If numbers are not discrete then they are said to be continuous, or uncountable.

In the situation of a coin flip, we can assign a 1 to the outcome of a head, and a 0 to the outcome of a tail. Thus we have transformed the outcome of a coin flip to a discrete random variable, or something that is countable and random.

Discrete distributions must always have probabilities between 0 and 1 and all probabilities must sum to 1.

In math this is

0 < = p(x) < = 1
and Sum(p(x)) = 1

Statistics, Basic Concept and Key Terms

The next series of days will focus on Statistics.

Statistics is the science and art of collecting, analyzing, and making conclusions about data. All data is collected from a set population. Subsets of the population can be called members, or units. If every subset of the population is collected, then we have a census, however, often just a small portion of the population is sampled. The sample is then thought to represent the whole population.

Care must be taken when choosing any given sample. For example, if we want to get an idea of how a population will vote on a new cigarette tax it does no good to sample non-voters like children. Also, the sample must be random in order to assure accurate results. If we only ask voters leaving a cigarette store, we are not likely to get good results and arrive to correct conclusions.