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Miklós Schweitzer 1955- Problem 3

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September 30, 2015

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Problem Statement

3. Let the density function

f(x)

of the random variable

\xi

bean even function; let further

f(x)

be monotonically non-increasing for

x>0

. Suppose that

D^{2}= \int_{-\infty }^{\infty }x^{2}f(x) dx

exists. Prove that for every non negative

\lambda

P(\left |\xi \right |\geq \lambda D)\leq \frac{1}{1+\lambda ^{2}}

. (P. 7)

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