The random variable X has a continuous uniform distribution on the interval from 1 to 7, that represents the waiting time, in minutes, to place your order at the favorite neighborhood coffee shop. Use this information to answer the following. Show your work. a) What is the height of the probability density function for X? Show your work. b) What is the expected value of X? Show your work. Explain in layperson terms what this means in the context of the problem. c) Calculate P(X 3). Work out by hand and confirm your answer using R. d) Calculate P(1 X 5). Work out by hand and confirm your answer using R. e) Calculate P(X = 7).