Limit Theorems Markovs Inequality Chebyshevs Inequality - PowerPoint PPT Presentation

Apr 04, 2023 •206 likes •250 views

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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