Understanding Chebychevs Inequality

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Chebyshev's inequality states that for any random variable, the probability that it deviates from the mean by more than k standard deviations is at most 1/k^2. In the expression P[|x-mu|>=ksigma], x represents the random variable, mu is the mean, and sigma is the standard deviation. To find the probability that a<x<b using this inequality, one must express a and b in terms of standard deviations from the mean. Understanding this relationship helps clarify how Chebyshev's inequality can be applied to specific ranges. The discussion highlights the importance of grasping the concepts of mean and standard deviation in probability assessments.
Mary89
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Hi, I am having trouble understanding Chebychevs inequality.

when it states P[|x-mu|>=ksigma]<=1/k^2, I don't really get what x-mu represents, For example if I wanted to know the probability that a<x<b, how would I use the inequality?

would I have to put a and b in terms of standard deviations?, is that what x-mu represents?

Thank you so much, anything that you can say about the inequality, even if it doesn't answer my specific question may help me to understand it better...
 
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