A taxi cab company has three taxis that operate from the airport. The time it takes for a taxi to take the customer to their destination is exponentially distributed with parameter u. Customers arrive according to a Poisson process with an average of rate 2. If a customer arrives when no taxi is available, they go to another taxi cab company. The taxis always return to their base station at the airport after dropping off a customer without picking up any new customers on their way back. a) Identify the states of the system, arrival and departure rates in each state, and draw the state transition diagram of the system.
b) Derive an expression of the probability that all the taxis are available.
c) What is the probability that an arriving customer goes to another taxi cab company?

In a study of the relationship between socio-economic class and unethical behavior, 129 university of california undergraduates at berkeley were asked to identify themselves as having low or high social-class by comparing themselves to others with the most (least) money, most (least) education, and most (least) respected jobs. they were also presented with a jar of individually wrapped candies and informed that the candies were for children in a nearby laboratory, but that they could take some if they wanted. after completing some unrelated tasks, participants reported the number of candies they had taken. it was found that those who were identiď¬ed as upper-class took more candy than others. in this study, identify: (a) the cases, (b) the variables and their types, (c) the main research question, (d) identify the population of interest and the sample in this study, and (e) comment on whether or not the results of the study can be generalized to the population, and if the ď¬ndings of the study can be used to establish causal relationships.