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Random Variables, Conditional Probability (contd.)

Random variables

Conditional Probability as a Random Variable

Independent Events

Zero Probability Events:

\[P(E) == 0\]
  • Not the same as impossible events.
  • These are relevant when dealing with uncountable sets where every outcome by itself has 0 probability and even some events have 0 probability but are not impossible. For example consider the sample space to be the interval [0,1] and then consider the event that the outcome of our experiment is a rational number. Since the rationals are countable because they can be written as a sequence. We can consider the event that the outcome is rational to be a union of disjoint sets with a rational number in each set.