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where the marginal, joint, and/or conditional probability density functions are denoted by with the appropriate subscript. This can be simplified as This can be simplified as
The joint distribution encodes the marginal distributions, i.e. the distributions of each of the individual random variables and the conditional probability distributions, which deal with how the outputs of one random variable are distributed when given information on the outputs of the other random variable(s).
is the relative entropy of the joint probability distribution (,) from the product () of the two marginal probability distributions — i.e. the expected number of extra bits that must be transmitted to identify X and Y if they are coded using only their marginal distributions instead of the joint distribution.
The joint information is equal to the mutual information plus the sum of all the marginal information (negative of the marginal entropies) for each particle coordinate. Boltzmann's assumption amounts to ignoring the mutual information in the calculation of entropy, which yields the thermodynamic entropy (divided by the Boltzmann constant).
where is the marginal benefit to each person of consuming one more unit of the public good, and is the marginal cost of providing that good. In other words, the public good should be provided as long as the overall benefits to consumers from that good are at least as great as the cost of providing it ( public goods are non-rival, so can be ...
Your marginal tax rate is the rate of tax you pay on the portion of your income that falls in the highest tax bracket that applies to you. The IRS adjusts its tax brackets for inflation annually.
Understanding effective and marginal … Continue reading → The post Effective vs. Marginal Tax Rate appeared first on SmartAsset Blog. Effective vs. Marginal Tax Rates for 2022
Joint and marginal distributions of a pair of discrete random variables, X and Y, dependent, thus having nonzero mutual information I(X; Y). The values of the joint distribution are in the 3×4 rectangle; the values of the marginal distributions are along the right and bottom margins.