Compound Poisson process: Difference between revisions

Revision as of 23:00, 9 December 2016

Revision as of 11:30, 14 March 2017

Line 11:

Using [[law of total expectation|conditional expectation]], 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(E(Y(D_{1} + ... + D_{N_{t}})|N = E(t))) = E(N(t))E(D)D_{1}) = = E(N(t))E(DD_{1}) = \lambda t E(D).</math>

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