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1.4 Exercise 22

Avg difficulty 2.5

Suppose $\left\{A_{1} , A_{2} , \hdots , A_{n}\right\}$ is a partition and $\left\{c_{1} , c_{2} , \hdots , c_{n}\right\}$ is a class of positive constants. For each event E, let

Q \left(E\right) = \sum_{i = 1}^{n} c_{i} P \left(E A_{i}\right) \left/\sum_{i = 1}^{n}c_{i}P\left(A_{i}\right)\right)

Show that $Q \left(\cdot\right)$ us a probability measure.

Pfeiffer, Applied Probability, 1.4 Problems on Probability Systems, exercise 22

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