Please help me with solving questions 1a, 1b and 1c. Provide all the steps to get to the final solution. Thanks a lot!

You decide to rank students based on their grades. Let X be the grade of a student. It can take the values \"Pass with distinction", \"Pass\" and \"Fail", which give 3, 2 and 1 points, respectively. Let Y be the gender of the student, which can take the values male or female, denoted m and I. For a population of students, the shares of males and females and the grade-points they get are presented in the table below. Let us treat X and 1" as random variables. Outcome Female (f) Male (m) 3 0.175 0.075 2 0.42 0.13 1 0.105 0.045 (a) What are the marginal distributions of X and Y? (b) What is the probability distribution of X. conditional on Y and the probability distribution of Y conditional on X? (c) Find E(X)