Thread: Marginal distribution

For the following joint distribution

---Y

X- 1-- 2
0 .02 .08
1 .11 .44
2 .07 .28

(i) Calculate the marginal distribution for each of X and Y
(ii) Find
a) P(X >= 1)
b) P(X = 1 | Y = 2)
(iii) Indicate if X and Y are independent, justifying your answer.

for i)
to find you just have to sum across the rows, so you get:





and for you do the same thing across the columns, so you get:



for ii)
a) so
b)

for iii)
they're dependent, but I'm still trying to figure out why.