Please explain how to solve part e, part f, and part g with a detailed explanation Thank you

W Let Y be a random variable representing income (in tons of thousands of dollars} and X be a. random variable representing years of education. Suppose that the marginal distribution of X is described by its probability mam function one if: 6 {1,2,. .._12} 0.09 if I e {13,14,15,1e} 0.04 if a: E {17} [1 otherwise me: = The marginal distribution of Y is described by its probability density function 0.1 nos 51:} eo)={ 5' . l} otherwise (c) Using ElYX] = 60 compute the covariance between V and X. Cov(X,Y). (:1) Calculate the correlation coefcient between X and Y. (e) What does this covariance tell us about the relationship between education levels and income? Is there a positive or negative association? (f) Should we interpret this result as a causal relationship between education and income? 'What are some reasons we may want to refrain from this interpretation? [3) A common inequality used in econometrics is the Cauchy-Schwarz inequality. It states that1 for any random variables X and Y, and anyr functions 9\" and h[-). iEls-{XJh-(YJJI s l'lelx/Elhz'll- Use this inequality to show why the correlation coefcient is bounded between negative one and one. 1 S on 51' (Hint: 11'! 9(3) = I - ex and le) = tr - or)