1. A movie theatre line has 200 people. The movie ticket costs 5 dollars and people pay with 5 dollar or 10 dollar bills with equal probability. Design a simulation study to calculate how many 5 dollar bills must the cashier have initially in order to have enough change at all times with a probability of 0.95. Hint: Use the rand function to simulate the method of payment 2. Two computers share a single printer. During a one hour period, at any moment and independently both computers will start a printing job (only one each computer). Each printing job last 20 minutes. A collision occurs if any of the two computers find the printer busy at the moment it sends its printing job. If there is a collision, the job that arrives the latest goes directly to the printing que and waits until the previous job finishes. Use a MATLAB simulation to calculate: 1) the probability of a collision, 2) the mean waiting time, and 3) the waiting time in the situations there is a collision. 3. Six perfect hunters shoot using a single independent shot at a group of six identical ducks (note that two or more hunters may shoot the same duck). One of the ducks has been identified for research purposes using an invisible chip. Use simulation to calculate: 1) the probability that the research duck will survive, 2) the expected (i.e. mean) number of ducks that will survive the shooting