Probability Theory

Probability-Theory

  1. Set Theory
  2. Probability Theory
  3. Conditional Probability and Independence
  4. Random Variables
  5. Distribution Functions

Set Theory

  • Countable set: it consists of countable number (finite or countably infinite) of elements. For example, the set of even numbers is countably infinite; the set of prime numbers under 10,000 is finite.

  • Uncountable set: it consists of uncountable number of elements. For example, the number of real numbers in any interval (a, b); the set of possible outcomes from measuring human weight or height.

Probability Theory

Experiments

  • Many investigations may be characterized in part by the fact that repeated experimentation.
  • Each experiment terminates with an outcome.
  • Suppose that we have such an experiment, the outcome of which can’t be predicted.
  • If this kind of experiment can be repeated under the same conditions, it is called a random experiment.
  • The collection of every possible outcome is called the experimental space or the sample space.
  • Event – a set of outcomes.

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