A consumer is trying to decide between two long-distance calling plans. The first one charges a...

A consumer is trying to decide between two long-distance calling plans. The first one charges a flat rate of 10 cents per minute. The second charges a flat rate of 99 cents for calls up to 20 minutes in duration and then 10 cents for each additional minute exceeding 20. (Assume that calls lasting a non-integer number of minutes are charged proportionately to a whole-minutes charge). If the duration of a randomly selected call of this consumer is exponentially distributed and its expected value is 15 minutes, compute the expected value of the corresponding charge by each plan.

Hint: Denote by X the duration of a random call, by Y1 the charge of the first plan, and by Y2 the charge of the second plan. Then, express Y1 and Y2 as functions of X, i.e., Y1 = h1(X) and Y2 = h2(X)

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milcah answered 3 weeks ago

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