The severity of a certain cancer is designated by one of the grades 1, 2, 3, 4 with being the least severe and the most severe. If X is the score of an initially diagnosed patient and the score of that patient after three months of treatment, hospital data indicates that p(i, j) = P(X = i, Y = j) is given by

a. Find the probability mass functions of X and of Y;

b. Find E[X] and E[Y].

c. Find Var(X) and Var (Y).

Transcribed Image Text:

Р(1,1) 3.08, Р(1, 2) — .06, Р(1,3) — .04, р(1,4) 3 02 p(2, 1) %3.06, р(2, 2) %3.12, р(2, 3) 3.08, р(2, 4) %3 .04 p(3, 1) %3D.03, р(3, 2) %3 09, р(3,3) %3D. 12, р(3,4) 3.06 Р(4, 1) %3.01, р(4, 2) %3D.03, р(4, 3) %3.07, р(4, 4) %3.09