

Uncertainties 
Uncertainty is a term
used in subtly different ways in a number of fields, including philosophy, physics, statistics, economics,
finance, insurance, psychology, sociology, engineering, and information science. It applies to predictions of
future events, to physical measurements already made, or to the unknown.  Wikipedia
Although the terms
[uncertainty and risk] are used in various ways among the general public, many specialists in decision theory,
statistics and other quantitative fields have defined uncertainty and risk more specifically. Doug Hubbard defines
uncertainty and risk as:
 Uncertainty: The lack of certainty, A state of having limited knowledge where it is impossible to exactly
describe existing state or future outcome, more than one possible outcome.
 Measurement of Uncertainty: A set of possible states or outcomes where probabilities are assigned to each
possible state or outcome  this also includes the application of a probability density function to continuous
variables.
 Risk: A state of uncertainty where some possible outcomes have an undesired effect or significant loss.
 Measurement of Risk: A set of measured uncertainties where some possible outcomes are losses, and the
magnitudes of those losses  this also includes loss functions over continuous variables.
Apply these rules for calculating uncertainties:
If with measured uncertainties then
If the uncertainties are independent and
random, then:

If with measured uncertainties then
If the uncertainties are independent and
random, then:

where the measured value of x = x ± dx 



