Conditional Expectation and Variance

In these expressions, E [X y and E Y. t] are considered as random variables and subscripts in Ex or Ey mean that expectation is taken with respect to x or y by using their respective marginals. The two last expressions are also known as total expectations. 

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Assume that too independent units were introduced initially into the system with a transfer mechanism whose hazard rate h applies to all units in the experiment. The random movement of individual units in the heterogeneous process will result in a state probability p (t, h) depending on the specific h of all units in that experiment. Using the binomial distribution, the conditional expectation and variance are... 

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