PROBABILTY DISTRIBUTION OF A DISCRETE RANDOM VARIABLE Suppose you have to cross a train track on your commute while driving your car from home to work. You estimate the chance that you have to wait for a train is 35 percent. If you don't have to wait for the train, the commute takes 15 minutes, but if you do have to wait, it takes 30 minutes. (a) Construct the probability distribution for the random variable defined as 'the length of time it takes you to commute to work' (3 marks) (b) Calculate E(X), and interpret this number in context. Show your calculations. (2 marks)