Poisson Distribution is a mathematical concept used to model the probability of a certain number of events occurring within a specific time or space interval. It is often used to predict the likelihood of rare events, such as the number of accidents in a day or the number of customers entering a store in an hour.
Poisson Distribution can be calculated using the formula P(x) = (e^-λ * λ^x)/x!, where λ is the average number of events that occur in the given interval and x is the number of events we are interested in.
Chebyshev's Inequality is a mathematical theorem that provides a lower bound on the probability that a random variable will deviate from its mean by a certain amount. It states that for any random variable with a finite mean and variance, the probability that the variable deviates from the mean by more than k standard deviations is at most 1/k^2, where k is any positive number.
Chebyshev's Inequality is used in statistics to determine the probability of extreme events occurring. It allows us to make statements about the probability of a random variable falling within a certain range, even when we do not know the exact distribution of the variable.
Yes, Chebyshev's Inequality can be applied to any distribution as long as it has a finite mean and variance. This includes both discrete and continuous distributions, making it a useful tool for analyzing a wide range of data sets.