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Joint Distribution Table

Consider the following joint distribution.

If the experiment is flipping a fair coin three times, which of the following could be the random variables \(X\) and \(Y\). Select all that apply.

  1. \(X=\) the number of heads, \(Y=\) the number of tails.
  2. \(X=\) the number of tails, \(Y=\) the number of tails (i.e., \(Y=X\)).
  3. \(X=\) the number of heads. \(Y=3-X.\)
  4. \(X=\) the number of tails on the first two flips. \(Y=\) the number of tails on the last two flips.

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