QUESTION THREE (a) The actual demand of a product for 6 months are summarized in Table below: Actual Demand Values i. ii. iii. iv. Month (1) V. 1 2 3 4 i. 5 6 Number of rainstorms (x) Number of stations (f) reporting x rainstorms ii. Find three months weighted moving averages by assuming the weights W, = 0.15, W = 0.36 and W = 0.49. Compute the mean forecast errors. Compute the mean square error Compute the mean absolute deviation. Mean absolute percent error (MAPE) (b) The table below gives the distribution for the number of heavy rainstorms reported by 330 weather stations in Zambia over one year period. Demand (D) 300 450 700 0 102 900 1200 1400 1 2 3 4 5 14 74 28 10 2 more than 5 0 Find the expected frequencies of rainstorms given by the Poisson distribution having the same mean and total as the observed distribution. Use the x distribution to test the adequacy of the Poisson distribution as a model for these data.