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The order in probability notation is used in probability theory and statistical theory in direct parallel to the big-O notation that is standard in mathematics.Where the big-O notation deals with the convergence of sequences or sets of ordinary numbers, the order in probability notation deals with convergence of sets of random variables, where convergence is in the sense of convergence in ...
where E is the expected value operator. Notably, correlation is dimensionless while covariance is in units obtained by multiplying the units of the two variables. If Y always takes on the same values as X, we have the covariance of a variable with itself (i.e. ), which is called the variance and is more commonly denoted as the square of the ...
Vector multiplication. In mathematics, vector multiplication may refer to one of several operations between two (or more) vectors. It may concern any of the following articles: Dot product – also known as the "scalar product", a binary operation that takes two vectors and returns a scalar quantity. The dot product of two vectors can be ...
Weak solution. In mathematics, a weak solution (also called a generalized solution) to an ordinary or partial differential equation is a function for which the derivatives may not all exist but which is nonetheless deemed to satisfy the equation in some precisely defined sense. There are many different definitions of weak solution, appropriate ...
Second moment method. In mathematics, the second moment method is a technique used in probability theory and analysis to show that a random variable has positive probability of being positive. More generally, the "moment method" consists of bounding the probability that a random variable fluctuates far from its mean, by using its moments.
Conjugate variables. Conjugate variables are pairs of variables mathematically defined in such a way that they become Fourier transform duals, [1][2] or more generally are related through Pontryagin duality. The duality relations lead naturally to an uncertainty relation—in physics called the Heisenberg uncertainty principle —between them.
Guard digits are also used in floating point operations in most computer systems. As an example, consider the subtraction . Here, the product notation indicates a binary floating point representation with the exponent of the representation given as a power of two and with the significand given with three bits after the binary point.
Enumerative combinatorics is an area of combinatorics that deals with the number of ways that certain patterns can be formed. Two examples of this type of problem are counting combinations and counting permutations. More generally, given an infinite collection of finite sets Si indexed by the natural numbers, enumerative combinatorics seeks to ...