STOCHATIC MODELS

Please answer the wole question. (show all steps).

(1) Statistical divergence between the sample-spaces of the RVs in X and Y expressed in terms of Kullback-Leibler (KL) measures, KLI and KL2. (2) Plot year-by-year profiles of (TRX X KLI versus r) and (TRY X KL2 versus r) and comment on the differences observed (3) Infer the stretch of time (in years) in which both X and Y perform almost closely in terms of their tariffs (4) Find Pearson-1 and -2 skewness coefficients between sample-spaces of RVs of X and Y (5) Suppose successive annual tariffs grow (or decline) in X and Y depending on previous year rate, decide the appropriate average performance in each case of X and Y in terms of AM or HM or GM. (Why?) (6) Indices for the tariff-rates for the years 2009-2018 Details: ESU X r =1 r = 2 r = 3 r = 4 r = 5 2009 2010 2011 2012 2013 Tariff-rate: Tx (RV) 72 56 69 83 75 ESU X in $ Frequency 172 160 162 122 100 of occurrences, (nr)x r = 6 r = 7 r = 8 r = 9 r = 10 2014 2015 2016 2017 2018 Tariff-rate: Tx (RV) 77 84 33 35 33 ESU X n $ Frequency 95 133 165 170 168 of occurrences, (nr)x\fQuestion # VII Two electric service utilities (ESUs), X and Y have charged their service areas country- wide at competitive tariff-rates (expressed in $) that change randomly over ten years, 2009-2018 (indexed as r = 1 through 10 for X and Y) as summarized below in the table. Relevant tariff-rates (T ) and (T ) shown depict RVs having corresponding frequencies of occurrence, (n ) and (n ), respectively. Hence, determine the following