Let X and Y have the joint pmf described as follows: (x, y): (0, 0) (0, 1) (1, 0) (1, 1) (2, 0) (2, 1) p(x, y):1/12, 5/

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Let X and Y have the joint pmf described as
follows:
(x, y): (0, 0) (0, 1) (1, 0) (1, 1) (2, 0) (2, 1)
p(x, y):1/12, 5/12, 2/12, 2/12, 1/12, 1/12
and p(x, y) is equal to zero elsewhere.
(a) Find the marginal pmf of Y . What is the name of
the
distribution of Y ?
(b) Find μ2 = E(Y ) and σ 2/2
= Var(Y ).
(c) [ Suppose that the mean of X is μ1 = 2/3

and the variance of
X is σ 2/1 =5/9
. Find the correlation coefficient ρ of X and Y .
(d) Find P(X + Y = 1).[