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A back-of-the-envelope calculation is a rough calculation, typically jotted down on any available scrap of paper such as an envelope. It is more than a guess but less than an accurate calculation or mathematical proof. The defining characteristic of back-of-the-envelope calculations is the use of simplified assumptions.
In that case the other envelope contains a/2 with probability 3/5 and 2a with probability 2/5. So either the first envelope contains 1, in which case the conditional expected amount in the other envelope is 2, or the first envelope contains a > 1, and though the second envelope is more likely to be smaller than larger, its conditionally ...
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Bertrand's box paradox: the three equally probable outcomes after the first gold coin draw. The probability of drawing another gold coin from the same box is 0 in (a), and 1 in (b) and (c). Thus, the overall probability of drawing a gold coin in the second draw is 0 / 3 + 1 / 3 + 1 / 3 = 2 / 3 .
3.2 Efficient infinite series. 3.3 Other infinite series. 3.4 Machin-like formulae. 3.5 Infinite products. 3.6 Arctangent formulas. 3.7 Complex functions.
These definitions E 1, E 2, and E 3 of the envelope may be different sets. Consider for instance the curve y = x 3 parametrised by γ : R → R 2 where γ(t) = (t,t 3). The one-parameter family of curves will be given by the tangent lines to γ. First we calculate the discriminant . The generating function is
The Snell envelope, used in stochastics and mathematical finance, is the smallest supermartingale dominating a stochastic process. The Snell envelope is named after James Laurie Snell . Definition
The group velocity is the rate at which the wave envelope, i.e. the changes in amplitude, propagates. The wave envelope is the profile of the wave amplitudes; all transverse displacements are bound by the envelope profile.