3. (10 points) Discrimination in the workplace is illegal, and companies that discriminate are often sued. The female instructors at a large university recently lodged a complaint about the most recent round of promotions from assistant professor to associate professor. An analysis of the relationship between gender and promotion produced the following joint probabilities. Promoted (X = 1) |Not Promoted (X = 0) Female (Y = 1) 0.3 0.1 Male (Y = 0) 0.2 0.4 Define X which takes 1 if an assistant professor is Promoted and 0 if an assistant professor is Not Promoted. Define Y which takes 1 if an assistant professor is Female and 0 if an assistant professor is Male. (a) What is the probability of promotion among female assistant professors? (b) What is the probability of promotion among male assistant professors? 4. (20 points) We are given the following probability distribution of X X =x 012 2 3 Pr (X = x) .1 .2 .3 .4 (a) What is the mode? (b) What is the median? (c) What is the mean? (d) What is the variance