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The global maximum of x √ x occurs at x = e. Steiner's problem asks to find the global maximum for the function =. This maximum occurs precisely at x = e. (One can check that the derivative of ln f(x) is zero only for this value of x.) Similarly, x = 1/e is where the global minimum occurs for the function
When "E" is used to denote "expected value", authors use a variety of stylizations: the expectation operator can be stylized as E (upright), E (italic), or (in blackboard bold), while a variety of bracket notations (such as E(X), E[X], and EX) are all used. Another popular notation is μ X.
It is tempting to think that in order to find the expected value E(g(X)), one must first find the probability density f g(X) of the new random variable Y = g(X).
e aX e bX = e (a + b)X; e X e −X = I; Using the above results, we can easily verify the following claims. If X is symmetric then e X is also symmetric, and if X is skew-symmetric then e X is orthogonal. If X is Hermitian then e X is also Hermitian, and if X is skew-Hermitian then e X is unitary.
Portable Document Format (PDF), standardized as ISO 32000, is a file format developed by Adobe in 1992 to present documents, including text formatting and images, in a manner independent of application software, hardware, and operating systems.
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If X is a given object of C, then we get a functor E X from A C to A by evaluating functors at X. This functor E X is exact. While tensoring may not be left exact, it can be shown that tensoring is a right exact functor: Theorem: Let A,B,C and P be R-modules for a commutative ring R having multiplicative identity.
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