What is Sigma: Definition and 228 Discussions

Sigma (uppercase Σ, lowercase σ, lowercase in word-final position ς; Greek: σίγμα) is the eighteenth letter of the Greek alphabet. In the system of Greek numerals, it has a value of 200. In general mathematics, uppercase ∑ is used as an operator for summation. When used at the end of a letter-case word (one that does not use all caps), the final form (ς) is used. In Ὀδυσσεύς (Odysseus), for example, the two lowercase sigmas (σ) in the center of the name are distinct from the word-final sigma (ς) at the end.

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  1. J

    B Sigma Multiplied Gaussian Distribution

    Hi! Say i have two variables that have independent gaussian distributions of probability of being a certain value when i sample them, what is the likely hood that both will land on a 3 sigma value simultaneously? Is there an equation that easily determines that? Also for other combinations like...
  2. J

    B Equation to approximate percent likelyhood of different sigma events

    Hi! I was wondering if there was an equation to plug in a standard deviation value and get back approximately the percent likely hood of getting that sigma (for example 1 sigma would be 33%, 3 sigma 0.27%, etc). Just something that approximates it with algebra, no calculus Thanks!
  3. U

    MHB Precalculus: What is the value of this sigma notation?

    Hi, I'm currently a Grade 11 student and I need help for this question (Precalculus): If $\sum\limits_{i=1}^{50} f(i)=90$ and $\sum\limits_{i=30}^{50} g(i)=60$, what is the value of $\sum\limits_{i=1}^{50} (7 g(i)-f(i)+12)/(2)$? P.S. To those who could answer this, it would be a great help...
  4. H

    Proof of a dot product using sigma notation

    Mentor note: Moved from a technical section, so is missing the homework template. Hi, I'm always not sure how to prove something in math and I'm wondering if this is enough. ##\vec r \cdot (\vec u + \vec v) ## ##\vec u + \vec v = (u_1+v_1, u_2+v_2,u_3+v_3) = \vec s## ##\vec r \cdot (\vec u +...
  5. mfb

    A Spectroscopy of positronium fine structure: 4.5 sigma deviation

    Precision Microwave Spectroscopy of the Positronium n=2 Fine Structure A nice compact abstract, so I'll just quote it here: Positronium with its two light leptons is the dream of every theorist, that keeps the uncertainties small. The 0.61 MHz experimental uncertainty are the sum of 0.57 MHz...
  6. Math Amateur

    MHB Smallest Sigma Algebra .... Axler, Example 2.28 ....

    I am reading Sheldon Axler's book: Measure, Integration & Real Analysis ... and I am focused on Chapter 2: Measures ... I need help in order to make a meaningful start on verifying the first part of Axler, Example 28 ... The relevant text reads as follows: Can someone please help me to make...
  7. Math Amateur

    I Smallest Sigma Algebra .... Axler, Example 2.28 ....

    I am reading Sheldon Axler's book: Measure, Integration & Real Analysis ... and I am focused on Chapter 2: Measures ... I need help in order to make a meaningful start on verifying the first part of Axler, Example 28 ... The relevant text reads as follows:Can someone please help me to make a...
  8. Math Amateur

    I Sigma Algebras .... Axler, Page 26 ....

    I am reading Sheldon Axler's book: Measure, Integration & Real Analysis ... and I am focused on Chapter 2: Measures ... I need help in order to fully understand the implications of Axler's definition of a ##\sigma##-algebra ... ... The relevant text reads as follows: Now in the above text...
  9. Math Amateur

    MHB Sigma Algebras .... Axler Page 26 ....

    I am reading Sheldon Axler's book: Measure, Integration & Real Analysis ... and I am focused on Chapter 2: Measures ... I need help in order to fully understand the implications of Axler's definition of a $\sigma$-algebra ... ... The relevant text reads as follows:Now in the above text Axler...
  10. F

    Which sigma algebra is this function a measure of?

    Suppose ##\nu## is a measure on some ##\sigma##-algebra ##\mathcal{A}##. Then we must have for all ##A \in \mathcal{A}## either ##A## or ##A^c## is finite, but not both. Because otherwise ##\nu(A)## is undefined or not well defined. I've verified that ##\lbrace \emptyset, X \rbrace## and...
  11. sysprog

    I Why is it possible for a sigma hyperon to decay into either 2 or 3 gamma hyperons?

    Why is it possible for a sigma hyperon to decay into either 2 or 3 gamma hyperons?
  12. F

    Infinite union of sigma algebras

    For all ##n\in\mathbb{N}## we have ##\emptyset \in A_n##. Hence, ##\emptyset \in \mathcal{A}_\infty##. Let ##A \in \mathcal{A}_\infty##. Then ##A \in A_k## for some ##k\in\mathbb{N}##. So ##A^c \in A_k##. Hence, ##A^c \in \mathcal{A}_\infty##. Thus, ##\mathcal{A}_\infty## is closed under...
  13. mfb

    I T2K sees ~3 sigma evidence for neutrino CP violation

    Publication: Constraint on the matter–antimatter symmetry-violating phase in neutrino oscillations Edit: arXiv: Constraint on the Matter-Antimatter Symmetry-Violating Phase in Neutrino Oscillations Article: Neutrino Asymmetry Passes Critical Threshold Previous measurements already hinted at...
  14. r12214001

    Bond energy of a Pi bond and a sigma bond

    It is well known that sigma bond is stronger than Pi bond. However in bond energy table that C=O is 745 KJ and C-O is 358 KJ. we can calculate the Pi bond energy is 745-358=387! The Pi bond(387KJ) is stronger than sigma bond(358KJ) ? How could this happen?
  15. P

    MHB Proving First Order Logic in Machover's Text

    Trouble working through Set theory, Logic, and their Limitations by Maurice Machover. Particularly these 1. $\sigma \vDash \alpha \rightarrow \forall x\alpha$ where $x$ does not occur in a free $\alpha$ 2. $\sigma \vDash s_1 = t_1 \rightarrow ... \rightarrow s_n = t_n \rightarrow...
  16. C

    How to compare two measurements with uncertainties in terms of sigma?

    Perhaps that statement is just saying how big the t-value is. Like, in this case: t = (1.0 - 0.98) / 0.1 = 0.1 So we can say that our measured value is within 1 sigma from the other measured value. In this case, do we just ignore the uncertainties of the other measured/reference value? It's...
  17. Zack K

    Calculating area using sigma notation

    Homework Statement The question involves using sigma notation of Riemann sums to find the area under the graph of ##x^2+\sqrt {1+2x}##. I managed to calculate most of the values and I have ##16+\frac 8 3 + \Sigma {\frac 2 n \sqrt {9 + \frac {4i} n}}## Homework Equations [/B] ##\Sigma i= \frac...
  18. K

    I Exploring Geometry: The $\star \sigma = 1$ Equation

    <Moderator's note: Moved from another forum.> The book I'm reading says that ##\star \sigma = 1## and ##\star 1 = \sigma##, but I'm not sure about the last one. The space is ##V = \mathbb{M}^4## and we choose the canonical base ##e_0,e_1,e_2,e_3##. This means that ##g_{ij} =...
  19. C

    MHB Math induction with sigma notation

    Prove by math induction that n sigma 3i + 1 = n/2 (3n + 5) i = n
  20. Cerenkov

    B How does 400 sigma compare with 5 sigma?

    Hello. On Ethan Siegel's 'Starts With a Bang' blog... http://scienceblogs.com/startswithabang/2010/06/28/how-do-we-use-the-cmb-to-learn/ ...he points out that the FIRAS CMB data has 400 sigma error bars. Since I've read that a 5 sigma value corresponds to a p-value of 3 x 10 -7 (approx. 1...
  21. jim mcnamara

    I MiniBooNE results at 6.1 sigma: Potential evidence for sterile neutrinos

    Bee Hossenfelder's blog has a discussion: http://backreaction.blogspot.com/ Preprint: https://arxiv.org/abs/1805.12028 New evidence in the search for the 'sterile' neutrino. Can someone comment on this please. @mfb
  22. C

    MHB Deducing Sigma (2r)^3 = 2n^2 (n+1)^2 | n, r=1

    Deduce that n Sigma (2r)^3 = 2n^2 (n+1)^2 r=1I'm not exactly sure how to start.
  23. N

    Mathematical Induction with Sigma notation

    Prove by mathematical induction that n sigma r^3 = n^2(n+1)^2/4 r = 1 so far I have 1 sigma r^3 = 1^2(1+1)^2/2 r=1 1 = 1(4)/2 1 = 4/2 1 = 2 I'm not sure what to do after this for the k+1 case.
  24. A

    I Significance of an excess calculated by the Asimov formula

    Is the significance of an excess calculated by Asimov formula given in units of sigma? Z_0 = \sqrt{2((s+b) ln(1+ s/b)-s)} where s are the signal events and b are the background events. If no, how can I calculate it in units of sigma? Thank you in advance!
  25. RoboNerd

    I Question about simplifying Sigma notation

    Hello everyone! I have this expression which I have to simplify: ∑i=1log(n) 1(log(n) - i) And my book apparently simplifies it to being log(n). I am struggling to figure out why this is the case. Could anyone help? Thanks!
  26. N

    How to appropriately assign sigma values (uncertainty)

    First let me preface this by saying, I'm not a native english speaker. I'm not sure "uncertainty" is the word I'm looking for it might also be deviation, however it is the translation of what its called in Danish, my native tongue. I'm doing a lab report about rolling objects on a slope, for my...
  27. I

    Is B2 a compound with no sigma bond but only a pi bond?

    Could suggest a compound with no sigma bond only with the pi bond?
  28. shihab-kol

    Sigma and Pi Bonds: Questions for Novices

    I am a novice and new to bonding and there are a few clarifications I need. 1) Does a single covalent bond always mean a sigma bond? 2) Does a double covalent bond always mean 1 sigma and 1 pi? 3) And does a triple covalent bond always mean 1 sigma and 2 pi bonds?
  29. J

    I On the decay of the neutral Sigma particle

    Hello! I wanted to ask why does the neutral Σ decay almost always to one γ(or two) and a neutral Λ. Why can't it decay to anything else? Thanks!
  30. binbagsss

    Weierstrass zeta & sigma fncts, pseudo-periodicity identity

    Homework Statement Let ##{w_1,w_2} ## be a basis for ##\Omega## the period lattice. Use ##\zeta (z+ w_{i})=\zeta(z)+ n_i## , ##i=1,2## ; ## m \in N## for the weierstrass zeta function to show that ##\sigma ( z + mw_i )=(-1)^m \exp^{(mn_i(z+mwi/2))}\sigma(z)## Homework Equations [/B] To...
  31. K

    I Decay of the Bs0 meson latest LHC results 7.8 sigma

    https://www.eurekalert.org/pub_releases/2017-04/thni-tma041217.php In its most recent analysis the LHCb experiment team took into account not only the first but also the second phase of operation of the LHC. The larger statistics helped achieve exceptional accuracy of the measurement of the...
  32. bluejay27

    I Representing sums as sigma notation?

    Hi is there a way or algorithm to find the sigma notation of sums in which the sums do not have an apparent general form?
  33. Singlau

    B Black hole mass and sigma (velocity dispersion)

    It seemed to have been asked before, but I am still a bit confused. How is the velocity dispersion formed? Doesn't the evidence of dark matter tells us that the orbital speed is uniform in a galaxy? Is there a direction of dispersion? (e. g velocity gets larger to the core) And why does...
  34. L

    Sigma notation and calculator help(casio fx9860g; ti-30xpro)

    Homework Statement A) use sigma notation and calculate sum as far as you wish (set your own endpoint)(1/2) + (1/4) + (1/8) + (1/16)...B) this is a personal problem because I want to know how to calculate the sums with e.g. sigma notation, with a calculator. Never having done this before...
  35. T

    Testing Six Sigma Green Belt Certification, CompTIA A+, & more

    Hi People, I'm being scheduled to take the Six Sigma Green Belt Certification exam sometime in the summer 2017. They already have the registration deadlines/dates up for 2017 already. It's an Open-book, open-notes, calculator-allowed test according to what I've been reading online. I'm...
  36. mfb

    I T2K: >2 sigma preference for neutrino CP violation

    Presentation at ICHEP Report at university website The main plot is on slide 18: ##\delta_{CP}## seems to be somewhere around -2, with 0 appearing unlikely. In other words, muon neutrinos oscillate more likely to electron neutrinos than anti-muon neutrinos oscillate to anti-electron neutrinos...
  37. Xico Sim

    I The spin-flavor wavefunction of Sigma+

    Hi, guys. If I want to write the spin-flavor wavefunction of ##\Sigma_+## starting only from knowing that the quark content of the proton is ##uud##, how can I procced? I started by applying the ladder operators in order to get the baryon octet vertexes. I am now having problems with...
  38. A

    MHB Sigma Algebra: Seeking Help on Closure & Countable Unions

    Hi everyone, didn't know where to post question on sigma algebra so here it is:- What I've tried till now: Let C\in G 1) For C=X, f^{-1}(B)=X which will be true for B=Y (by definition) 2) For closure under complementation, to show C^{c}\in G. So, C^{c}=X\setminus C=X\setminus...
  39. Kefeng

    Question about CMA-ES step size sigma

    Hi everyone, I am new here. I am working in geophysics and I would like to invert for a simple layered velocity model using CMA-ES optimization method. I downloaded the purecmaes.m code in Matlab here: https://www.lri.fr/~hansen/cmaes_inmatlab.html, and also implemented one in Fortran 90. I...
  40. Karan Punjabi

    Does B2 Have a Sigma Molecular Orbital?

    Guys I studied Molecular orbital theory based on wave mechanics in lower level as i don't know what is wave mechanics so i saw molecular orbital diagram of boron di atomic molecule in which there are two pi molecular orbitals so my first question was that there must be first a sigma molecular...
  41. S

    Total significance Higgs discovery at 7+8TeV LHC

    HI guys, a quick question. After the announcement of the discovery of the higgs-like resonance in July 2012 with ~5sigma significance by both ATLAS and CMS, what is the current p-value distribution with the full data set taken into account? And therefore, what is the total significance reached...
  42. S

    Increasing sequence of sigma algebras

    The explanation of a continuous Markov process X(t) defines an indexed collection of sigma algebras by \mathcal{F}_t = \sigma\{ X(s): s < t\} and this collection is said to be increasing with respect to the index t . I'm trying to understand why the notation used for set inclusion is...
  43. M

    MHB Normal distribution question: determine sigma

    The lengths of a certain species of worm follow a normal distribution. Thirty percent of the worms are at least 16cm long, and 15% of the worms are less than 10cm long. Find, to 2 decimal places, the standard deviation of the lengths of the worms.
  44. A

    How can I convert sigma notation into a finite geometric series?

    Homework Statement http://postimage.org/][/PLAIN] image url Homework Equations N/A The Attempt at a Solution I have to solve a different question using a similar method to this one but I cannot figure out how they got the sigma notation into the last equation format. I tried writing out the...
  45. T

    Meaning of sigma in a 2D sigma

    Case 1: I have a 2D Gaussian: ## Ae^{-[\frac { (x-x_o)^2 }{2 \sigma_x ^2} + \frac { (y-y_o)^2 }{2 \sigma_y ^2}]} ## where ## \sigma_x \neq \sigma_y ## (at least not necessarily). Using this as my 2D Gaussian, would the normalization constant be ## A = \frac {1}{2\pi (\sigma_x ^2 + \sigma_y ^2)}...
  46. R

    Difference between Z notation and sigma

    Homework Statement What is the difference between this statement being expressed in z-notation and the notation shown? What are the benefits of the two and how do you do the conversion? Nevermind about answering the question itself. if X ~N(mu,sigma) show that P(|X-mu|<= 0.675*sigma) = 0.5...
  47. H

    Feynman rules for nonlinear sigma models

    Nonlinear sigma models are particular field theories in which the fields take values in some nontrivial manifold. In the simplest cases this is equivalent to saying that the fields appearing in the lagrangian are subject to a number of constraints. Since the lagrangian fields are not independent...
  48. Safinaz

    Exploring Sigma Regions for Observable R(D) in Theoretical Models | 1206.2634v2

    Hi all, I'd like to understand what does it mean by allowed 1 or 2 ## \sigma ## regions for some observable, like R(D) in Fig. 1 left [ 1206.2634v2] ? And how can I calculate or plot this value or region according to any theoritical model .. Bests.
  49. M

    Structure of generated sigma algbra

    I am think what is the structure of generated ##\sigma##-algebra. Let me make it specific. How to represent ##\sigma(\mathscr{A})##, where ##\mathscr{A}## is an algebra. Can I use the elements of ##\mathscr{A}## to represent the element in ##\sigma(\mathscr{A})##?