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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:

Sums and Differences
with measured uncertainties then

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

If the uncertainties are independent and random, then:
where the measured value of x = x ± dx