Stat help please! Joint probability mass function and covariance.

1. Suppose X and Y are random variables deﬁned on the same sample space with the following joint probability mass function. The goal of this problem is to arrange that Cov(X, Y ) = 0 but X and Y are independent.

X / Y -1 0 1
0 a b c
1 d e f

Here we assume that a, b, c, d, e, f are real numbers between zero and onesuch that a + b + c + d + e + f = 1.
(a) Give an example of a, b, c, d, e and f so that
Cov(X, Y ) = 0.

Question

Stat help please! Joint probability mass function and covariance.

1. Suppose X and Y are random variables deﬁned on the same sample space with the following joint probability mass function. The goal of this problem is to arrange that Cov(X, Y ) = 0 but X and Y are independent.

X / Y   -1    0    1
0          a     b    c
1          d     e    f

Here we assume that a, b, c, d, e, f are real numbers between zero and onesuch that a + b + c + d + e + f = 1.
(a) Give an example of a, b, c, d, e and f so that
Cov(X, Y ) =  0.