Limit Theorems Markovs Inequality Chebyshevs Inequality - - PowerPoint PPT Presentation

▶

Apr 04, 2023 206 likes •251 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

SLIDE 1

IE502: Probabilistic Models IEOR @ IITBombay

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.

SLIDE 2

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?

SLIDE 3

IE502: Probabilistic Models IEOR @ IITBombay