Compound Poisson process: Difference between revisions

Revision as of 11:31, 14 March 2017

Revision as of 11:33, 14 March 2017

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The [[expected value]] of a compound Poisson process can be calculated using a result known as [[Wald's equation]] as:

:<math>\,E(Y(t)) = E(D_{1} + ... + D_{N_{N(t})}) = E(N(t))E(D_{1}) = E(N(t))E(D) = \lambda t E(D).</math>

Making similar use of the [[law of total variance]], the [[variance]] can be calculated as: