There's a homework problem in my text that asks me to select an (odd) integer randomly from the set {1,3,5,7} and call it X. Then select an integer randomly from the set {0,1,2,3,4} add it to X. and then let Y be this sum.

(a) how can you show the joint p.m.f. of X and Y on the sample space of X and Y? I have drawn a table and labeled the axis accordingly, and matched up each sum and computed the sum at their intersection?


(b) How could one compute the marginal p.m.f.’s?

(c) and are X and Y independent? Reasons? I wrote yes but I'm not sure why.
Any help is appreciated thank you very much.

(a) What are the possble values of Y? How do you get them for each value of X? Therefore what probability is in each cell?
(b) Use the definition. Where do you get stuck?
(c) Is there any pair such that Pr(X = x).Pr(Y = y) does not equal Pr(X=x and Y=y)?

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