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Problem 389

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Platonic Dice

An unbiased single 4-sided die is thrown and its value, T, is noted.
T unbiased 6-sided dice are thrown and their scores are added together. The sum, C, is noted.
C unbiased 8-sided dice are thrown and their scores are added together. The sum, O, is noted.
O unbiased 12-sided dice are thrown and their scores are added together. The sum, D, is noted.
D unbiased 20-sided dice are thrown and their scores are added together. The sum, I, is noted.
Find the variance of I, and give your answer rounded to 4 decimal places.

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柏拉图多面体骰子

掷一个无偏的正四面体骰子，记点数为T。
掷T个无偏的正六面体骰子，记点数和为C。
掷C个无偏的正八面体骰子，记点数和为O。
掷O个无偏的正十二面体骰子，记点数和为D。
掷D个无偏的正二十面体骰子，记点数和为I。
求I的方差，并将你的答案四舍五入到4位小数。

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