5. SIMULATION PROBLEM A representative of a high-speed Internet provider calls customers to assess their satisfaction with the service. It takes her 6 seconds to turn on a phone and dial a number; then 3 additional seconds to detect a busy signal, or 25 additional seconds to wait for 5 rings and conclude that no one will answer; and 1 second to end a call. After an unsuccessful call, she re- dials (in the course of several days) until the customer answers or she has dialed four times. The outcome of each dialing is determined in an identical way: the customer being called is using the line with probability 0. 2; or is unavailable to answer the call with probability 0.3; or is available and can answer the call within X seconds, which is a continuous random variable with the mean of 12 seconds and the exponential distribution. Let W denote the total time spent by the representative on calling one customer. Your objective is to estimate several statistics of W. Toward this end, perform the following. 1. Formulate a model of the calling process. 1.1 Dene notation for all the elements of the model. 1.2 Write the expression for the cumulative distribution lnction of X, and derive the expression for its inverse. 1.3 Draw the tree diagram of the calling process. Him: The tree diagram may include \"if" statements and loops (like a owchart does)