Stochastic models for computer science

please show all the steps

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 r) 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 cach 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 Ir- r-2 -3 -4 r s 2009 2010 2011 2012 2013 Tariff-rate: TX (RV) 72 56 69 83 ins Frequency 172 160 162 122 of occurrences, in r= 10 r=6 r7 2014 2015 7784 r=8 2016 33 r=9 2017 35 Tariff-rate: TX (RV) ins 95 133 Frequency Jof occurrences, in Details: ESU Y Indices for the tanf-rates for the years 2009-2018 Ir-2 r=3r -4 -5 2009 2010 2011 2012 2013 72 5370 2 0 25 Tariff-rate: T (RV) in s 172 158 165 182 Frequency Jof occurrences, 2018 r6 r7 r8r=9 2014 2015 2016 2017 Tariff-rate: T (RV) 21 22 34 38 ins Frequency 188 148 155 172 jor occurrences, FSU Y (Answer hints: Mode of T, -21: Median of T - 70.5) 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 r) 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 cach 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 Ir- r-2 -3 -4 r s 2009 2010 2011 2012 2013 Tariff-rate: TX (RV) 72 56 69 83 ins Frequency 172 160 162 122 of occurrences, in r= 10 r=6 r7 2014 2015 7784 r=8 2016 33 r=9 2017 35 Tariff-rate: TX (RV) ins 95 133 Frequency Jof occurrences, in Details: ESU Y Indices for the tanf-rates for the years 2009-2018 Ir-2 r=3r -4 -5 2009 2010 2011 2012 2013 72 5370 2 0 25 Tariff-rate: T (RV) in s 172 158 165 182 Frequency Jof occurrences, 2018 r6 r7 r8r=9 2014 2015 2016 2017 Tariff-rate: T (RV) 21 22 34 38 ins Frequency 188 148 155 172 jor occurrences, FSU Y (Answer hints: Mode of T, -21: Median of T - 70.5)