The click probability distribution for the web traffic to a publisher's web site has a mean of 0.01. The publisher would like to enter into a contract with an ad-network (such as Chitika) with a click-through-rate guarantee of 0.9%. What value of a click probability threshold (the decision variable ?) should be used to obtain maximum clicks while ensuring the required click-through-rate constraint is achieved.

b) If the click probabilities for a publisher lie between 0 and 0.02, is it possible to use some value of a threshold (?) so as guarantee that a click-through-rate of 0.03 will be achieved?

Consider the following 10 probability values (probability of a click for an arriving visitor) for a certain publisher. There are 10 classes of visitors, and each class is equally likely.

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