Stewart Dunn
08/21/2023 · Primary School
29. Let \( X \) be a random variable with probability density function \( f(x)=\left\{\begin{array}{ll}\frac{5}{x^{6}}, & x>0 \\ 0 & \text { otherwise }\end{array}\right. \). What bound does Chebyshev's inequality give to the probability \( P(X>2.5) \) ?
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The mean of the random variable \( X \) does not exist, so we cannot calculate the variance or use Chebyshev's inequality to find the bound for \( P(X>2.5) \).
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