Consider the University of California, Berkeley (UCB) admissions data discussed in class, and explored in the simpsons.paradox.r example. (a) Construct and print the two-way table of the department and the admit status, as well as a mosiac plot of the table. Do department and the admit status appear independent? Argue for your answer. (b) Construct and print the two-way table of department and gender, as well as a mosiac plot of the table. Do these variable appear independent? Justify your answer. (c) Construct a two-way table of gender and admit status for the applicants to deparment F and create its mosaic plot. For the applicants to department F do gender and admit status appear to be independent? (This question could be rephrased to ask if admit status and gender conditionally independent given department F). (d) Create a l-way table of the gender of Rejected students (without regard for department).