Packets arrive at a queue at the rate of 1 per minute The qu

Packets arrive at a queue at the rate of 1 per minute. The queue is not emptied until 7 packets arrive. Let the packet interarrival times be exponentially distributed and let X be time to fill the queue. Obtain the probability that more than 10 minutes elapse until the queue is emptied. In a wireless automatic meter reading system, a base station sends out a wake-up signal to nearby electric meters. On hearing the wake-up call signal, a meter transmits a message indicating the electrical energy usage. Each message is transmitted eight times. If a single transmission of a message is successful with probability 0.8, what is the PMF of N, the number of successful messages transmitted? What is the probability of 7 successful transmissions?

Solution

5.

P(X>10)=e^10lambda=e^10*1/7=0.20