1. Explain with your own words what is a random variable and a random process.
2. Explain with your own words and give an example of the following kind of random processes:
The LUT restaurant works from 9 to 14. Based on the data, there were identified three different periods in relation to arrival of people to have lunch. Answer the following 3 questions.
Hint: Careful with the time scales given in the question and the one implemented in the tutorial.
3. The arrivals follow a Poisson process with different arrival rates (see below). Simulate it, plot the historgram from the simulated results and compare with the analytical formulation. These are the parameters.
NOTE: Compute using rates in students per minute.
4. Using the code from the tutorial, simulate these three scenarios (one scenario per cell, do not combine the three scenarios in the same code). In this case, the restaurant put more works so the service rate varies as follows.
NOTE 1: Compute using rates in students per hour as input of the code.
NOTE 2: Simulation time is 2 hours.
NOTE 3: The analytical formulation only works when the queue is stable, i.e. arrival rates lower than service rates
5. Discussions about the results.
Challenge (not to be graded). Simulate a more realistic queue system considering that the three periods are sequencial and that the last period only ends after the last service is complete. When the restaurant is closed?