Question # VII Two electric service utilities (ESUS), X and Y have charged their service areas country- wide at competitive tariff-rates (expressed in S) 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 (Ty) and (Ty) shown depict RVs having corresponding frequencies of occurrence, (ne)x and (n)y respectively. Hence, determine the following: (1) Statistical divergence between the sample-spaces of the RVs in X and Y expressed in terms of Kullback-Leibler (KL) measures, KL1 and KL2. (2) Plot year-by-year profiles of (Trx KL1 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) Details: ESU X Indices for the tariff-rates for the years 2009-2018 r=1 r=2 =3 1=4 1=5 2009 2010 2011 2012 2013 72 56 69 8375 ESU X Tariff-rate: Tx (RV) in S Frequency of occurrences. (1.)x 172 160 162 122 100 1=6 2014 77 1=7 2015 8 4 158 159 1= 10 2016 2017 2018 33 35 33 ESU X Tariff-rate: Tx (RV) in S Frequency of occurrences. (1.)x 95 133 165 170 168 Details: ESU Y Indices for the tariff-rates for the years 2009-2018 r=1 r= 21=3 r=4r=5 2009 2010 2011 2012 2013 72 537020 25 ESU Y Tariff-rate: Ty (RV) in s Frequency of occurrences, (n.) 172 158 165182180 1=6 2014 21 1=7 2015 22 158 2016 34 1=9 2017 38 1= 10 2018 33 ESU Y Tariff-rate: TY (RV) in s Frequency of occurrences. (11.) 188 148 155 172 165 (Answer hints: Mode of Ty= 21: Median of T. = 70.5) Question # VII Two electric service utilities (ESUS), X and Y have charged their service areas country- wide at competitive tariff-rates (expressed in S) 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 (Ty) and (Ty) shown depict RVs having corresponding frequencies of occurrence, (ne)x and (n)y respectively. Hence, determine the following: (1) Statistical divergence between the sample-spaces of the RVs in X and Y expressed in terms of Kullback-Leibler (KL) measures, KL1 and KL2. (2) Plot year-by-year profiles of (Trx KL1 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) Details: ESU X Indices for the tariff-rates for the years 2009-2018 r=1 r=2 =3 1=4 1=5 2009 2010 2011 2012 2013 72 56 69 8375 ESU X Tariff-rate: Tx (RV) in S Frequency of occurrences. (1.)x 172 160 162 122 100 1=6 2014 77 1=7 2015 8 4 158 159 1= 10 2016 2017 2018 33 35 33 ESU X Tariff-rate: Tx (RV) in S Frequency of occurrences. (1.)x 95 133 165 170 168 Details: ESU Y Indices for the tariff-rates for the years 2009-2018 r=1 r= 21=3 r=4r=5 2009 2010 2011 2012 2013 72 537020 25 ESU Y Tariff-rate: Ty (RV) in s Frequency of occurrences, (n.) 172 158 165182180 1=6 2014 21 1=7 2015 22 158 2016 34 1=9 2017 38 1= 10 2018 33 ESU Y Tariff-rate: TY (RV) in s Frequency of occurrences. (11.) 188 148 155 172 165 (Answer hints: Mode of Ty= 21: Median of T. = 70.5)
