In a production environment, let random variable X be the number of parts produced on a given day, and Y be the number of defectives out of X parts. X takes values from the set {0,1,2,3} such that all the elements are equally likely,and the distribution of Y conditioned on X is the following:

( = | = )	X = 0	1	2	3
Y = 0	1	0.9	0.81	0.729
1	0	0.1	0.18	0.243
2	0	0	0.01	0.027
3	0	0	0	0.001

a. Write the joint distribution of X and Y.

b. Calculate ( = 3 | = 2).

PLEASE HELP ALL QUESTONS A-B