stochatic models

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Question # 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 (TX) and (T) shown depict RVs having corresponding frequencies of occurrence, (n.), and (n), 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 KLI versus) and (T, 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: ESUX r-1-2 2009 2010 72 56 -3 2011 69 -4 2012 83 rs 2013 Tariff-rate: TX (RV) ins Frequency of occurrences, in 172 160 162 122 r=6 r7 r8 2014 2015 2016 7784 33 r=9 2017 35 r=10 2018 Tariff-rate: TX (RV) in s 95 133 170 Frequency Jof occurrences, in Indices for the tanf-rates for the years 2009-2018 Details: ESU Y -I r -2 2009 2010 72 5370 r=3 2011 2 0 =4 = 5 2012 2013 Tariff-rate: T (RV) in S Frequency Jof occurrences, 172 158 165 182 r6 r7 r8 r9 r10 2014 2015 2016 2017 Tariff-rate: T (RV) 21 22 34 38 ins Frequency 185 145 155 172 of occurrences, (n. FSU Y (Answer hints: Mode of T, -21: Median of T-705) Question # 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 (TX) and (T) shown depict RVs having corresponding frequencies of occurrence, (n.), and (n), 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 KLI versus) and (T, 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: ESUX r-1-2 2009 2010 72 56 -3 2011 69 -4 2012 83 rs 2013 Tariff-rate: TX (RV) ins Frequency of occurrences, in 172 160 162 122 r=6 r7 r8 2014 2015 2016 7784 33 r=9 2017 35 r=10 2018 Tariff-rate: TX (RV) in s 95 133 170 Frequency Jof occurrences, in Indices for the tanf-rates for the years 2009-2018 Details: ESU Y -I r -2 2009 2010 72 5370 r=3 2011 2 0 =4 = 5 2012 2013 Tariff-rate: T (RV) in S Frequency Jof occurrences, 172 158 165 182 r6 r7 r8 r9 r10 2014 2015 2016 2017 Tariff-rate: T (RV) 21 22 34 38 ins Frequency 185 145 155 172 of occurrences, (n. FSU Y (Answer hints: Mode of T, -21: Median of T-705)