Probability in the Engineering and Informational Sciences
Likelihood Ratio Ordering Of The Inspection Paradox
Probability in the Engineering and Informational Sciences
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Suppose that there are n families with children attending a certain school and that the number of children in these families are independent and identically distributed random variables, each with probability mass function P{X = j} = pj, j ≥ 1, with finite mean &mgr; = ∑j≥1 jpj. If a child is selected at random from the school and XI is the number of children in the family to which the child belongs, it is known that limn→∞ P{XI = j} = jpj /&mgr;,j ≥ 1. Here, asymptotic expansions for P{XI = j} are developed under the condition E|X|3