Random Errors

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Random Errors

• Random (accidental) errors are those errors
  remaining after systematic errors have been
  eliminated.
• Characteristics Positive and negative with same
  occurrence probability for same absolute value of
  the signal.
• Less probable as magnitude of the absolute value
  increases.

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Random Errors

• Approaches zero as the number of measurements
  increase.
• For a given measurement method, random errors do
  not exceed a fixed value. If random errors do
  exceed a fixed value, that experiment should be
  repeated and studied separately.

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Random Errors

• Random errors imply one measures n times to have
  a set of x (datum) that can be averaged (xn) . If
  the set of values is finite then each average is
  different. The averages follow a Gaussian
  Distribution
• Having a variance of s2/n and s2 is the variance
  of x.
• Confidence interval for x is
• xn uncertainty x xn uncertainty

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Random Errors

• And the uncertainty is k times the square root of
  the variance or
• ks/vn
• One can obtain k from the tables of the normal
  Gaussian Distribution tables.
• The confidence interval has a probability of
• Conf. Interval Probability 1 a where a is
  also found from the Gaussian Distribution tables.
  

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Random Errors

• The normalized Gaussian Distribution is shown at
  the following site
• http//www.itl.nist.gov/div898/handbook/eda/sectio
  n3/eda3661.htm
• In normalized functions, the total probability
  is 1. So 1-a is the total probability minus the
  tail of the Gaussian Distribution.

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Random Errors

• See Example 1.2 page 19 of the text.

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