Limit Theorems Markovs Inequality Chebyshevs Inequality - PowerPoint PPT Presentation

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Limit Theorems Markovs Inequality Chebyshevs Inequality Importance Allows us to derive bounds on probabilities when only the mean or only the mean and variance of the distribution is know. IE502: Probabilistic Models

Limit Theorems • Markov’s Inequality • Chebyshev’s Inequality • Importance – Allows us to derive bounds on probabilities when only the mean or only the mean and variance of the distribution is know. IE502: Probabilistic Models IEOR @ IITBombay
Limit Theorems (contd.) • Strong Law of Large Numbers • Central Limit Theorem • Example: Lifetime of a battery is random variable with mean 50 hours and std. dev of 25 hours. A battery is used until it fails, at which time it is replaced with a new one. Suppose 10 batteries are available, the lifetimes of which are independent. What is the probability that over 550 hours of use can be obtained? IE502: Probabilistic Models IEOR @ IITBombay
IE502: Probabilistic Models IEOR @ IITBombay

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