Moodle | Learning M X Th Spring 2023-MATHE X wk Course Hero X Y! sum of geometri ser X y.' sum of geometric 50 X 64: Sum of a Series X e unit7 (2).pdf C' Q 2. A model of social mobility in England was published by Glass and Hall tracking profession across generations. They grouped all professions into seven \"classes\" and found the fraction of children from each class that grew up to be in each class. From this data, they created a Markov Chain with the transition matrix and steady state probability vector given below. The classes are arranged as high classes rst and lower classes last. a) Is the transition matrix a positive matrix? A regular matrix? Justify your answers (don't try to multiply T by itself a bunch of times). b) What assumptions are implicit in making this a linear stationary Markov chain. Briey justify those assumptions, or nd reasons to discount them? What do you think of this model as a model of social mobility? c) At the steady state, what is the predicted percentage in class 5? d) The current percentage in each class is also given below. Make an argument that this data supports the idea that social mobility follows a linear stationary Markov chain. The following matrix/ vector entries are written as percentages. 38.8 10.7 3.5 2.1 0.9 0.0 0.0 14.7 26.7 10.1 3.9 2.4 1.3 0.8 20.2 22.7 18.8 11.2 7.5 4.1 3.6 6.2 12.0 19.1 21.2 12.3 8.8 8.3 14.0 20.7 35.7 43.1 47.3 39.1 36.4 4.7 5.3 6.7 12.4 17.1 31.2 23.5 1.6 2.0 6.1 6.2 12.5 15.5 27.4 Steady P3; = [2.3 4.18.8127 41018.2 12.9] Current PT = [3.0 4.6 9.4 13.1 40.9 17.0 12.1]