California subsidizes within-state tuition of students who has a high school GPA of 3 or above (CAL grant) as long as they submit a federal financial aid application. Suppose you want to understand how receiving this grant affects students' college going probability using regression discontinuity.

1. Will you need to use a sharp regression discontinuity method or a fuzzy regression discontinuity method? Why?
2. Write down the estimating equation(s). Which coefficient would give you the effect of receiving this grant on students' college going probability?
3. What are the assumption(s) needed for regression discontinuity method to give us valid estimates? Be specific. How can you test the assumption(s)?
4. Can this method tell us how students with high school GPA of 3.8 are affected by the program?