[Below is the statement of the "sandwich shop problem" (25 points). Please show your work for each part in the answer sheet. Also, enter your final numerical answers in the spaces provided below. Please enter your final answers in decimal format, up to two decimal points in accuracy.] You are hired by a sandwich shop, "Sooubway", to help them decide how many Sandwich Artists they need to hire at their branch near OSU campus. You decide to run a simulation, and as a first step, you sit at the store one day recording data about customers' arrivals. You observe 120 customers, and record the following inter-arrival times (in minutes) for them: Inter-arrival time Observed number of customers [0,2) 30 (2,4) 18 [4.6) 30 [6.8) 42 You decide to model the inter-arrival times as a continuous random variable, X. Part (a) (15 points): Find the empirical CDF of X, as a piece-wise linear function. For this part, it is enough to plot the CDF, clearly indicating the start and end points of each line segment (i.e., you do not need to find the equations of all these line segments explicitly in this part). Part (b) (10 points): Using the inverse transform method, generate a sample from this empirical CDF. In answering this question, assume the output of your random number generator is 0.23. [Below is the statement of the "sandwich shop problem" (25 points). Please show your work for each part in the answer sheet. Also, enter your final numerical answers in the spaces provided below. Please enter your final answers in decimal format, up to two decimal points in accuracy.] You are hired by a sandwich shop, "Sooubway", to help them decide how many Sandwich Artists they need to hire at their branch near OSU campus. You decide to run a simulation, and as a first step, you sit at the store one day recording data about customers' arrivals. You observe 120 customers, and record the following inter-arrival times (in minutes) for them: Inter-arrival time Observed number of customers [0,2) 30 (2,4) 18 [4.6) 30 [6.8) 42 You decide to model the inter-arrival times as a continuous random variable, X. Part (a) (15 points): Find the empirical CDF of X, as a piece-wise linear function. For this part, it is enough to plot the CDF, clearly indicating the start and end points of each line segment (i.e., you do not need to find the equations of all these line segments explicitly in this part). Part (b) (10 points): Using the inverse transform method, generate a sample from this empirical CDF. In answering this question, assume the output of your random number generator is 0.23