Airlines sometimes overbook flights (that is, they sell more tickets than there are seats on the plane). Suppose that for a plane with 50 seats, the airline has sold 55 tickets. Define the random variable X as the number of ticketed passengers who actually show up for the flight. The probability distribution function of X is shown in the table below. x 45 46 47 48 49 50 51 52 53 54 55 p(x) 0.05 0.10 0.12 0.14 0.28 0.17 0.06 0.02 0.03 0.02 0.01 Calculate E(X), the expected number of ticketed passengers who show up for the flight.

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