Theorems in statistics | Theory of probability distributions | Statistical laws | Algebra of random variables

Law of total cumulance

In probability theory and mathematical statistics, the law of total cumulance is a generalization to cumulants of the law of total probability, the law of total expectation, and the law of total variance. It has applications in the analysis of time series. It was introduced by David Brillinger. It is most transparent when stated in its most general form, for joint cumulants, rather than for cumulants of a specified order for just one random variable. In general, we have where * κ(X1, ..., Xn) is the joint cumulant of n random variables X1, ..., Xn, and * the sum is over all partitions of the set { 1, ..., n } of indices, and * "B ∈ π;" means B runs through the whole list of "blocks" of the partition π, and * κ(Xi : i ∈ B | Y) is a conditional cumulant given the value of the random variable Y. It is therefore a random variable in its own right—a function of the random variable Y. (Wikipedia).

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Simplify rational expression using the rules of exponents

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Simplify an expression by applying quotient rule of exponents

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From playlist Simplify Using the Rules of Exponents | Quotient Rule

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From playlist Simplify Using the Rules of Exponents | Quotient Rule

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Simplify a rational expression by using properties of exponents

👉 Learn how to simplify expressions using the quotient rule of exponents. The quotient rule of exponents states that the quotient of powers with a common base is equivalent to the power with the common base and an exponent which is the difference of the exponents of the term in the numerat

From playlist Simplify Using the Rules of Exponents | Quotient Rule

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Simplifying an expression using properties of exponents

👉 Learn how to simplify expressions using the quotient rule of exponents. The quotient rule of exponents states that the quotient of powers with a common base is equivalent to the power with the common base and an exponent which is the difference of the exponents of the term in the numerat

From playlist Simplify Using the Rules of Exponents | Quotient Rule

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Simplifying a rational expression using the property of exponents

👉 Learn how to simplify expressions using the quotient rule of exponents. The quotient rule of exponents states that the quotient of powers with a common base is equivalent to the power with the common base and an exponent which is the difference of the exponents of the term in the numerat

From playlist Simplify Using the Rules of Exponents | Quotient Rule

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Related pages

Law of total variance | Random variable | Independence (probability theory) | Law of total probability | Expected value | Moment (mathematics) | Mathematics | Probability theory | Time series | Partition of a set | Statistics | Central moment | Poisson distribution | Normal distribution | Cumulant | Law of total expectation