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Prove that it is impossible for two independent identically distributed random variables, X₁ and X₂, each taking the values I to 6, to have the property that P[X₁ + X₂ = k] = -1/11 for k = 2, 3, ... , 12. Consequently, conclude that it is impossible to weight a pair of dice so that the probability of occurrence of every sum from 2 to 12 will be the same.

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Category:- Statistics and Probability
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