Question: Long-distance calling plan A offers a flat rate service at 10 cents per minute. Calling plan B charges 99 cents for every call under 20 minutes; for calls over 20 minutes, the charge is 99 cents for the first 20 minutes plus 10 cents for every additional minute. (Note that these plans measure your call duration exactly, without rounding to the next minute or even second.) If your long-distance calls have exponential distribution with expected value [itex] \tau [/itex] minutes, which plan offers a lower expected cost per call? Answer: I am lost. Here is my attempt. We first want a random variable that yields the cost for each plan. Lets first let [itex] T [/itex] be a random variable that represent the time of the call. Thus, [tex] C_A = 10 T [/tex] A random variable of cost is representative of the random variable for the cost of the time. Now, I don't really know how to do plan B, here is my attempt: [tex] C_B = 99 + 10(T-20)u(T-20) [/tex] where [itex] u(T-20) [/itex] would be the step function. I am trying to say that the [itex] 10(T-20) [/itex] term would turn on at [itex] T \geq 20 [/itex]. Now I want the expected value of each, thus: [tex] E(C_A) = 10 \tau [/tex] [tex] E(C_B) = 99 + 10E((T-20)u(T-20)) [/tex] I am lost, and need help. Thanks!