For random variable T in Quiz 2.6, first find the expected value E[T] using Theorem 2.10. Next,…

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For random variable T in Quiz 2.6, first find the expected value E[T] using Theorem 2.10. Next, find E[T] using Definition 2.14.

Quiz 2.6

Monitor three phone calls and observe whether each one is a voice call or a data call. The random variable N is the number of voice calls. Assume N has PMF

Voice calls cost 25 cents each and data calls cost 40 cents each. T cents is the cost of the three telephone calls monitored in the experiment. (1) Express T as a function of N. (2) Find PT (t) and E[T ].

Theorem 2.10

Given a random variable X with PMF PX (x) and the derived random variable Y = g(X), the expected value of Y is