1. A smart meter updates the status of the electricity

1. A smart meter updates the status of the electricity usage every 12 hours to the central controller. It sends out an indictor message wirelessly and the message is received at the controller with probability p. If the message is received successfully then the controller sends a ACK message to the smart meter. For errored reception NAK message is sent. The ACK/NAK message is received with probability q. It is known that p = 0:9 and q = 1 for this communication network scenario. If NAK message is received then the smart meter sends the same indicator message again and the maximum number of times such repeated message sending is allowed is K. Assume independent message transmission. If correct message is not received after K attempts (including the original one) the controller alerts the network operator to take action. (a) If K = 2 what is the probability that the network operator has to act on this meter reading? (b) If the probability of alerting the network operator has to be less than 0.01% how many attempts should be tried. (c) Discuss the trade-off of communication cost and technician cost. 2. Let X be the input to a communication channel and let Y be the output. The input to the channel is +1 volt or -1 volt with equal probability. The output of the channel is the input plus noise voltage N that is uniformly distributed in the interval -2 volts to +2 volts. Find P[X = +1; Y _ 0]. 3. A communication system accepts a voltage V and outputs a voltage Y = _V + N where _ = 10?2 and N is Gaussian random variable with parameters m = 0 and _ = 2. Find the voltage value of V that gives P[Y

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