Question: 6. Let 1/9 (a) Show that the probability mass function of X + Y is the convolution function of the probability mass functions of X

6. Let −1/9

Y T -1 0 1 -1 1/9 0 1/9+c 1/9 c 1/9+c

(a) Show that the probability mass function of X + Y is the convolution function of the probability mass functions of X and Y for all c.

(b) Show that X and Y are independent if and only if c = 0.

Y T -1 0 1 -1 1/9 0 1/9+c 1/9 c 1/9+c 1/9 1/9-c 11/9-c 1/9+c 1/9

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