Computing Expectation by Conditioning

  • Basic Idea: Compute the expectation or variance of a (complicated)  random variable by conditioning on another random variable.
  • In stochastic process, it is often useful to condition on the first event
  • Use of the formula
    • E[X] = E[E[X|Y]]
    • var[X] = var[E[X|Y]] + E[var[X|Y]]

Example:




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