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We flip a fair coin. If it is a head, we roll a die $n$ times, and if it is a tail, then we sample a number $n$ times with replacement from $\{1,2,3,4\}.$ The resulting random variable $X_1 X_2 \dots X_n$ is then exchangeable but not independent.

I know that for different permutation of $X$, we need to show they have the same mass function, but how do we find the PMF? Thanks

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Hint: Condition on the result of the coin-flip.

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