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Miklós Schweitzer 1984- Problem 9

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September 5, 2016
college contestsprobabilityfunction

Problem Statement

9. Let X0,X1,…X_0, X_1, \dots be independent, indentically distributed, nondegenerate random variables, and let 0<α<10<\alpha <1 be a real number. Assume that the series
∑k=1∞αkXk\sum_{k=1}^{\infty} \alpha^{k} X_k
is convergent with probability one. Prove that the distribution function of the sum is continuous. (P. 23) [T. F. Móri]
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