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Both Tom and Jane flip a fair coin twice. Let T be the number of heads Tom got, and J be the number of heads

Both Tom and Jane flip a fair coin twice. Let T be the number of heads Tom got, and J be the number of heads Jane got. Define Z as the sum of the heads both Tom and Jane got.

(a)Develop the joint probability distribution between T and Z.

(b)Are T and Z independent of each other? Why?

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