Let X be a random variable with values in [0, 1] and let Y be a random variable with values in [0, 1, 2].
Initially, we have the following partial information about their joint probability mass function:
Y
0 1 2
X 0
1 1/8 1/8

Subsequently, we are provided with the following information:
(i) Given X = 1, Y is uniformly distributed.
(ii) p_(X|Y) (0|0) = 2/3.
(iii) E[Y |X = 0] = 4/5.
Use this information to fill in the missing values of the joint probability mass function table.