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11

Part of 2012 Miklós Schweitzer

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Miklós Schweitzer 2012 P11

Source: Miklós Schweitzer 2012 P11

8/20/2018
Let X1,X2,..X_1,X_2,.. be independent random variables with the same distribution, and let Sn=X1+X2+...+Xn,n=1,2,...S_n=X_1+X_2+...+X_n, n=1,2,.... For what real numbers cc is the following statement true: P(∣S2n2n−c∣⩽∣Snn−c∣)⩾12P\left(\left| \frac{S_{2n}}{2n}- c \right| \leqslant \left| \frac{S_n}{n}-c\right| \right)\geqslant \frac{1}{2}
college contestsMiklos Schweitzerprobabilityreal analysis