The table below presents estimated probabilities for work arrangements for different level of education.3 % of employed adults saying that, regardless of their current work arrangement, for the most part, the responsibilities of their job

Can not be done from home (NH) Can be done from home (H)

HS or less (HSL) .83 (NH). .17(H)

0.83 0.17 Some college/associate (SCA) .71 (NH) .29 (H)

0.71 0.29 Bachelor (B) .42 (NH) .58 (H)

0.42 0.58 Postgrad (PG) .32 (NH) ? (H)

In addition, it is known that the probability that a workers educational attainment is high school or less is 0.32, whereas for a bachelor degree is 0.24. Finally, the probability that a worker can do most of her/his work at home is 0.38.

(a) What type of probabilities is the table displaying? Explain (2 points)

(b) Find the probability that is missing in the table. Show your work (2 points)

(c) What is the probability that a randomly selected worker can not do most of their job from home? Explain. Is this a marginal, conditional or joint probability? (2 points)

(d) What is the probability that a randomly selected worker can not do most of their job from home and has an educational attainment not higher than high school? Is this a marginal, conditional or joint probability? (3 points)

(e) Using the definition of independents events, are work arrangements and educational attainment independent variables? Explain. (2 points)

(f) Based on you answer in question (e), could you conclude that the educational attainment causes the work arrangement that a worker can obtain? Explain. (2 points)

(g) Can you recover the entire joint distribution for educational attainment and work arrangement? If you can, show the table with the calculated join probabilities. Otherwise, say what joint probabilities can not be calculated. (3 points)