14 The duration Y of long-distance telephone calls (in minutes) monitored by a station is a random variable with the properties that P(Y= 3) = 0.2 and P(Y= 6) = 0.3. Otherwise, Y has a continuous density function given by f(x) = √²/ve- 0, ye-y/3, min y > 0, elsewhere. The discrete points at 3 and 6 are due to the fact that the length of the call is announced to the caller in three-minute intervals and the caller must pay for three minutes even if he talks less than three minutes. Find the expected duration of a randomly selected long-distance call in minutes.

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