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Dice Probabilty : Convolving Probability Mass Functions ( PMF )

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There's 4 6-sided dice rolled independently. Set Y1 to be sum of the numbers on the first and second dice, Y2 to be sum of numbers on the third and fourth dice.

Convolve PMFs of Y1 & Y2 to find the probability of the outcome of the 4 rolls summing to be 8.

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Solution Summary

PMFs are convolved. The solution is detailed and well presented.