## How to convert a table of probabilities to j.p.d.f

Among the sudent that attempted the exams of Calculus III (CIII) and Differential Equation (DE) is oberved that the joint probability of passing or failing the exams is given by the following table:

__________________CIII
________________fail_______pass

DE______fail______0.3_______0.1

________pass_____0.1_______0.5
Given a student, let X be the r.v. that describes his result in DE and Y the r.v. that describes his result in CIII. Both variables take value 0 or 1 where 0 mean fail and 1 pass.

I have to compute the marginal pdf, conditional pdf, and corr(x,y)

in order to compute the marginal, i know i need to write a j.p.d.f in equation form with parameters for X and Y. Usually the book will give you the jpdf and you just differentiate it ect ect.

My question is, how would you convert a table like the one above into an equation that looks something like this:

______|__ 24xy -----------x>0,y>0
f(x,y) |
______|___0---------------otherwise