Suppose you want to study the relationship between educational attainment and the class or worker using the variables SCHL and COW. In order to do that, you classify the educational attainment variable in THREE categories: High school or less ( 17 ) , Some college-no degree or Associate degree (18-20 ), and Bachelor degree and beyond ( 21). Workers are classified as: Private (1-2), Public (3-5), and Self-employed (6-9). (a) Define the sample space for the joint events that results from the educational attainment and class of worker status outcomes. (4 points) (b) Use the dataset and R to prepare a table of an estimated joint probability distribution for the joint events defined in question (i).(15 points) 1A worker has been defined as someone who had a positive salary in the last 12 months previous to the interview. 2Source: The American Community Survey Public Use Microdata Sample. 1 (c) Use the joint probabilities found in (b) to compute the probability that a randomly selected worker has a bachelor degree or beyond. Is this a marginal, conditional or joint probability? (4 points) (d) Use the joint probabilities found in (b) to compute the probability that a randomly selected worker has a bachelor degree or beyond if: i. she/he works for a private organization or company, ii. she/he works in the public sector, iii. she/he is self-employed. Are these marginal, conditional or joint probabilities? (7 points) (e) Based on the probabilities that you found in question (c) and (d) and the definition of independents events, are the class of worker and educational attainment independent variables? Explain. (4 points) (f) Based on you answer in question (e), could you conclude that the educational attainment causes the class of the worker or viceversa? Explain. (2 points)