Question# 2: Complete the following sentences: 1) If the random process X(t) represents the total number of events occurred in the interval [0, t) then, the X(t) is called a 2) The Interarrival times for the Poisson process are identical independent --------- distributed. 3) Poisson Process has an ----- and -------- increments. 4) X(t)-X(s) in a Poisson Process represent that the number of events occurred in the interval is 5 events. 5) Poisson process {X(t)lt 0} is a counting process which X(t) are ------- and .. values. 3. A yoga studio opens a site in a small town. As the only yoga studio in its market, it would have market power, i.e. to sell larger quantities, it would have to set lower prices. (a) The demand curve for memberships at the studio is P = 30 - Q for Q300 and P = 0 for Q> 300 where Q denotes number of memberships and P the price. Draw the demand curve for memberships at the in the (Q, P) co-ordinates (Q on horizontal axis). How many memberships can be sold at P = 20? (b) The fixed cost of running the studio is 700. A yoga instructor costs 300 to hire and each instructor can serve up to 50 members. Draw the cost curve for the gym. (c) Draw the average cost curve for the studio. Is it possible to operate the studio profitably? (d) What is the optimal price for a profit maximizing studio? How many instructors should be hired? (Hint: What is the marginal revenue for the studio?). - Select your answer - What type of pattern exists in the data? - Select your answer - b. Develop the three-week moving average forecasts for this time series. Compute MSE and a forecast for week 7 (to 2 decimals if necessary). MSE The forecast for week 7 c. Use a = .2 to compute the exponential smoothing forecasts for the time series. Compute MSE and a forecast for week 7 (to 2 decimals). MSE The forecast for week 7 d. Compare the three-week moving average approach with the exponential smoothing approach using a = .2. Which appears to provide more accurate forecasts based on MSE? - Select your answer - e. Use a smoothing constant of a = .4 to compute the MSE (to 2 decimals). # Does a smoothing constant of .2 or .4 appear to provide more accurate forecasts based on MSE? The exponential smoothing forecast using a = .4 provides a Select your answer - forecast than the exponential smoothing forecast using a = .2 since it has a smaller MSE. Check My Work