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Here I summarise the rules of probability calculus. They have been
stated above; here they are grouped together, so they can be found
easily.
- Probability is a number between 0 and 1:
- If the outcome is certain, the probability of that outcome is
1: If is the probability for the variable , if
and only if takes the value .
- Definition of conditional probability: The conditional
probability is defined by this formula
- The probability that a variable takes one of a set of mutually
exclusive outcomes is the sum of the probability of the outcomes:
if can take
no more than one of the values
.
- The probability of independent events is computed by multiplying
the probability of each event:
if taking
the value does not depend whether or not takes the value .
- Bayes Rule:
- Bayes Rule (alternative form):
- Distribution of a single variable from the joint distribution:
One can find the distribution for from the joint distribution of
and by summing over all values of ,
The single distribution determined from the joint is called the
marginal distribution; this process is called marginalisation. Note:
It is not possible to infer the joint distribution from the
marginals.
Next: What is the Meaning
Up: A Primer on Probability
Previous: Conditional Probabilities are of
Jon Shapiro
1999-09-23