Sociologists have long been interested in social mobility - the transition of individuals between social classes defined on the basis of income or occupation. Consider a society with three social classes. Each individual may belong to the lower class (state 1), the middle class (state 2), or the upper class (state 3). Thus, the social class occupied by an individual in generation t may be denoted by s, E {1,2,3). suppose that intergenerational mobility is described by the transition matrix P 0.5 0.3 0.2 0.2 0.7 0.1 0.1 0.3 0.6 a. Determine the transition diagram from this transition matrix b. Write and run an R code to find the long term trend of the transition matrix c. What will be the proportions of lower, middle and upper class in long run