Markov's Inequality
Markov's Inequality is a fundamental result in probability theory that provides a way to estimate the probability of a random variable being greater than a certain value. Specifically, it states that for any non-negative random variable X and any positive number a, the probability that X is greater than or equal to a is at most the expected value of X divided by a. In mathematical terms, this is expressed as P(X ≥ a) ≤ E[X] / a.
This inequality is particularly useful because it requires minimal information about the distribution of X. It does not assume any specific distribution shape, making it applicable in various fields such as statistics, finance, and machine learning. Markov's Inequality serves as a foundational tool for more advanced concepts in probability and statistics.