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. L

    What is the appropriate sigma value for statistical significance?

    I'm working on a project where I have about 120,000 sources and my supervisor has told me to work out what significance to use for taking results. I had set it at 3 sigma. But there's roughly 1 in 500 chance that we will get a 3 sigma result by chance. I've been looking for a table to compare...
  2. W

    Express a series in sigma notation

    Homework Statement I've been given the series 3,4,6,10,18... and asked to express as the ∑ar, between r=0 and r = infinity. Homework EquationsThe Attempt at a Solution Well, I can see a pattern! The difference between terms doubles every time. I'm having difficulty expressing this...
  3. A

    Is the Definition of Sigma Algebra Limited to Countable Unions?

    1. Are uncountable unions of sigma algebras on a set X still a sigma algebra on X? 2. Are uncountable intersections of sigma algebras on a set X still a sigma algebra on X? (I think this statement is required to show the existence of sigma algebra generated by a set) 3. If 2 is true, can we...
  4. A

    Allowable stress in my project

    I'm doing a little project which came to a stop. I calculated expected material stress to be ~10 MPa. (bending) I know that my material (AlMgSi0,5) should carry well that stress, however I'm interested in max allowable stress for this material...
  5. C

    Equation of SNR versus sigma square for BPSK

    I would like to know in the following equation (attached) how can I incorporate BER for BPSK? is BER the same as Rc? The equation is relation between SNR and sigma square.
  6. T

    Why do only even values of n show up in the expansion of sin4x?

    Homework Statement Hello, I found this problem in the book I borrowed from the library, but this book does not have solutions in the back...I tried to lent the solution book but the library does not have it...so could someone help me out? The question is: It is possible to decompose the...
  7. S

    Transformations for the non-linear sigma action

    For the non-linear sigma action, S_G=\frac{1}{4\pi\alpha^\prime}\int d^2\sigma\sqrt{-\gamma(\sigma)}\gamma^{\mu\nu}(\sigma)G_{ij}(X)\partial_\mu(\sigma) X^i\partial_\nu X^j(\sigma), Let us consider an infinitesimal target space transformation X^\mu\to X^{\prime\mu}(X)=X+\epsilon\xi^\mu(X). The...
  8. A

    Extracting sigma from sum of distributions with moving mean

    I have an experiment in which I want to extract the distribution function of a process. I expect it to be Gaussian. Each data point measured is an entire distribution, f(x), but I am forced to average over many points such that the result of the experiment is the sum of many measurements of...
  9. A

    How Do You Resolve Negative Indices in Convolution Calculations?

    Hey, I've begun going through a book called "An introduction to geophysical exploration" by Phillip Kearey and Michael Brooks and I've come across a problem I can't for the life of me see how they got their answer. Essentially, given an input function gi (i = 1,2... m), and a convolution...
  10. T

    16 bit sigma delta ADC question

    Hi every one, I am examining a prototype device that is designed to analyse current from an electrochemical O2 sensor (current source), The sensor will output 1.124 uV per PPM (cross 47 ohms @0.023 uA), and has acuracy of +- 2 PPM, with max 1000 PPM. it ueses 16 bit Sigma Delta ADC with...
  11. D

    Total number of C-C sigma bond in phenylethene

    Homework Statement how many is total number of C-C sigma bond in phenylethene? Homework Equations The Attempt at a Solution i have drawn the the strucutre as in the photo. i ended up getting 8 C-C sigma bond. but the ans from my book is 12. How to get 12?
  12. P

    Molecular orbitals sigma and pi

    hi! i have a doubt, how can i know the total number of bonding and antibonding electrons given a diatomic molecule's electronic configuration in therms of sigma and pi orbitals? I have to add these σ and π orbitals are of the type gerade and ungerade. does anyone can help me?
  13. Conservation

    Sigma and Pi Bonds for Diatomic Oxygen Molecule

    According to the Molecular orbital theory, diatomic oxygen should have σ2px (internuclear axis) and \pi2py and \pi2pz orbitals filled with two unpaired electrons, one at antibonding \pi2py and the other at antibonding \pi2pz. And of course, the 2s bonding and antibonding orbitals as well...
  14. D

    MHB Value of Sigma such that the integral converges

    What value of sigma guarantees the integral converges? \[ \int_0^{\infty}e^{-5t}e^{-(\sigma + i\omega)t}dt = \frac{1}{5 + \sigma + i\omega} \] I don't see a problem as long as \(\omega\neq 0\) and \(\sigma\neq -5\), but by the way the question is worded, it sounds like it is after something else...
  15. P

    MHB Polynomial including Sigma Notation

    Hello everyone! I have this polynomial: $p(x) =$ 1 + \sum_{k=1}^{13}\frac{(-1)^k}{k^2}x^k - I'm supposed to show that this polynomial must have at least one positive real root. - I'm supposed to show that this polynomial has no negative real roots. - And I'm supposed to show that if $z$ is...
  16. B

    Question on Sigma Algebras and Non-Finite Sets

    Homework Statement Find a set X such that \mathcal{A}_1 \text{ and } \mathcal{A}_2 are \sigma-algebras where both \mathcal{A}_1 \text{ and } \mathcal{A}_2 consists of subsets of X. We want to show that there exists such a collection such that \mathcal{A}_1 \cup \mathcal{A}_2 is not a...
  17. W

    Is Lean Six Sigma Certification Worth the Effort?

    I currently work in semiconductors (research) and I am interested in earning my Lean Six Sigma certification, possibly through a university online class. Has anyone gone through the process? If so, what is the level of difficulty to obtain a green belt? I have a solid background in statistics...
  18. K

    Using sigma sums to estimate the area under a curve

    Homework Statement My apologies in advance for the messiness of the equations; the computers available to us do not correctly process the LaTex code. I am tasked with estimating the area under the curve f(x)=x2+1 on the interval [0,2] using 16 partitions. Online calculators and my...
  19. H

    Product Sigma Algebra Problem

    Homework Statement Given 3 measure spaces (X,A,\mu), (Y,B,\zeta), (Z,C,\gamma), show that the product of the three sigma algebras A, B, and C is associative, meaning that: AxBxC=(AxB)xC=Ax(BxC) Homework Equations We can make use of the fact that XxYxZ=(XxY)xZ=Xx(YxZ) The Attempt at a...
  20. R

    MHB Approximation property with F sigma and G delta Sets to show a set is measurable

    Prove that a set $A\subset\mathbb{R}^n$ is (Lebesgue) measurable $\iff$ there exist a set $B$ which is an $F_{\sigma}$ and a set $C$ which is a $G_{\delta}$ such that $B\subset A\subset C$ and $C$~$B$ (C without B) is a null set. $F_{\sigma}$ is a countable union of closed sets, and...
  21. W

    Sigma Algebra on Omega (Sample Space)

    Respected Members, Suppose Ω is the set of eight possible outcomes of three coin tosses i.e. Ω={{HHH, HHT, HTH, HTTT, THH, THT, TTH, TTT} So if we are not told the results then the sigma algebra ( denoted by F_α) at position α=0 is F_0 = {∅, Ω} Now if are told the first coin toss only...
  22. Superposed_Cat

    Can a Sigma Sum be Integrated with Fubini's Theorem?

    How would you Integrate a Sigma Sum?
  23. 8

    Mathematica Mathematica, Plot Implicit function contain Sum (sigma)

    Dear friends, Over the past week, I tried to plot implicit function by mathematica but failed. I am very disappointed. Hopefully someone help me at this time. My equation is given by (see below figure): Where z0 := 6 d := 12 k := 11800 w0 := 0.025 w[z_] := sqrt[w0^2*(1 + (z/z0)^2)]...
  24. J

    Sigma Notation and Product Notation

    Homework Statement Notice that ln [∏(k=1)^n a^k] = Ʃ_(k=1)^n * ln (a_k) I couldn't get the LaTeX right on this ^ But k=1 is below the product sign, and n is above. And (a^k) is the formula. From this, as well as some calculus, calculate that: lim as n->∞ ∏_(k=1)^n e^\frac{k^2}{n^3} For...
  25. Lebombo

    Can this be written in sigma notation: a + ar + ar^2 + + ar^n-1?

    Homework Statement a_{1}r^{1} + a_{1}r^{2} + a_{1}r^{3} +... + a_{1}r^{n-3} + a_{1}r^{n-2} + a_{1}r^{n-1} = \sum_{n=1}^{?} a_{1}r^{n-1} What value would replace the "?" 2. The attempt at a solution EDIT: I edited this post after receiving your reply Cepheid. My gut would say...
  26. MarkFL

    MHB Serina's questions at Yahoo Answers regarding sigma notation

    Here are the questions: Here is a link to the questions: How do you write the summation notation for: 4 - 24 + 144 - 864 + ... ? - Yahoo! Answers I have posted a link there so the OP can find my response.
  27. C

    What does it mean if my result is off the known value by one Sigma?

    I'm putting together a lab report and my result is off from the known value by 1.43 σ. According to the error function tables provided by my prof, and using the error function in my error analysis textbook, that gives me a probability of ~85%. I don't understand what this means though. Will...
  28. M

    Why do we have sigma and pi bonds?

    Hello, I am looking at the sigma and pi bonds and trying to understand them. I know that the bond is the overlap of the orbitals, in the case of sigma bonds two s-orbitals and the pi bonds is the p-orbitals. When you have the sp hybrid orbitals, how are there only the same number of hybrid...
  29. D

    Sigma Plot, Non-linear regression, fitting a line to a set of points

    I model arterial baroreflex data that I have collected in humans using the Kent equation which is: y=p1/(1+exp((x-p3)*p2))+p4; where Y=heart rate, X= estimated carotid sinus pressure, p1=range of Y, p2=slope coeff, p3=centerpoint on X, p4 = minimum Y. I use Sigma Plot to do a best fit line...
  30. M

    Proof of a set is sigma finite

    Homework Statement if f is integrable, then the set N(f) = {x : f(x)≠ 0} is \sigma-finite Homework Equations i am stucked in this proof , somebody help me pleaseThe Attempt at a Solution if f is simple the it seems the set is finite since otherwise the the integral won't exist but how can it...
  31. D

    Linear Sigma Model Invariance Under O(N)

    In addition to my Faddeev-Popov Trick thread, I'm still tying up a few other loose ends before going into Part III of Peskin and Schroeder. I was able to show that the other Lagrangians introduced thus far are indeed invariant under the transformations given. But, I am hung up on what I think...
  32. nomadreid

    P(x=mean) of normal PDF with low sigma - not allowed?

    P(x=mean) of normal PDF with low sigma -- not allowed? About the normal probability distribution: with formula P(X=x) = (1/(σ*sqrt(2π))*exp(-(x-μ)2/2σ2), what happens when you look at P(X=μ) if σ<(1/sqrt(2π))? You get P(X=μ)>1, an absurdity. What is going on? Second question is one about...
  33. H

    How to write taylor series in sigma notation

    Homework Statement My Calc II final is tomorrow, and although we never learned it, it's on the review. So I have a few examples. Some I can figure out, some I cant. Examples: f(x)=sinh(x), f(x)=ln(x+1) with x0=0, f(x)=sin(x) with x0=0, f(x)=1/(x-1) with x0=4 The only one of those that I was...
  34. B

    Evaluating the sum of a sigma notation problem with a lower limit k=10

    How do I evaluate the sum of this sigma notation problem? 20 ∑ k k=10 Normally, I would think to use the theorem for the sum of the first n integers: n ∑ k = n(n+1)/2 k=1 I don't know how to do this, however, since the lower limit is k=10, not k=1. My professor wrote this note on the board...
  35. O

    Sigma Algebras on [0,1]: Understanding Measures and Sub-Intervals

    This topic came up while studying measures on sub-intervals of [0,1]. The collection of all intervals in [0,1] is a semi-algebra, say J. Now from finite disjoint union of members of J let's say we form a set A. I was able to prove that A is an algebra, since for any C,D ε A, C\capD and C^{c}...
  36. H

    Sigma matrices question Group theory

    Homework Statement I have read the following text in a textbook(look the attaxhement) ,and i have a simple question .WHY every 2x2 hermitian matrix would have to satisfy this Equation.It is not obvious to me why.Does anyone know the answer? The textbook stops there without giving any...
  37. C

    What does the word-final sigma symbol mean in maths?

    Hi all, I have spent a good half hour searching for the meaning of this, but have only found results for upper-case sigma Ʃ and lower-case sigma σ. Can anyone tell me the meaning of the "word-final" version of sigma, which looks like ζ ? I am trying to evaluate 3ζ(4) but I just need a...
  38. T

    Sigma Plus Particle,baryon, question

    Homework Statement A sigma plus,\sum+ particle is a baryon a)How many quarks does sigma plus contain? b)If one of these particles is an s quark, by what interaction will it decay? c)Which baryon will it eventually decay into? b]solution attempt [/b] Baryons contain 3 quarks don't know...
  39. alane1994

    MHB Calculate Sigma Sums in Excel for Large n

    Is anyone familiar enough with excel to use it to find the sum in of sigma notation when "n" is large? \Sigma^{40}_{k=1} \sqrt\frac{3k-3}{4} Something like this?
  40. H

    Why can't the indefinite integral be written with sigma notation?

    Hi, I've been wondering this since I started learning integration. I get that ∫ is basically an elongated S for "sum", because that is what it is basically doing. But then Ʃ does the same thing as well. If I'm understanding the difference, it is that Ʃ increments by finite measures, whereas ∫...
  41. B

    Matrix Multiplication and sigma notation

    Hello, I have read several different sources on this very topic, and the one thing that confused a little was defining it using sigma notation. Could some please explain to be what it means?
  42. S

    Can Properties of Sigma Notation Prove Equivalence of Two Sums?

    Homework Statement Prove that: \sum_{n=1}^{14} 10n = \sum_{n=1}^{7} (20n+70) Homework Equations properties of sigma notation The Attempt at a Solution I know several properties of sigma notation but none that I know can be used to prove this. I don't know how to change 10 n to 20...
  43. X

    Indicate no of sigma and pi bonds

    Homework Statement find total sigma and pi bonds in c6h6 Homework Equations Benzene structure The Attempt at a Solution if i consider benzene structure, then total will be 12σ and 3∏ but according to the random structure that i managed to draw, it showed, 11σ and 4∏, was i wrong...
  44. I

    Proving \{0\} is an Element of Sigma Algebra Generated by A_n on \mathbb{R}

    Homework Statement Suppose \Omega = \mathbb{R}. Let A_n = [0,\frac{1}{n}]. Let \mathcal{A}=\{A_n:n\in\mathbb{N}\}. Is \{0\} an element of \mathcal{F}=\sigma(\mathcal{A})?Homework Equations The Attempt at a Solution Clearly \lim_{n\rightarrow\infty} A_n = \{0\}. Not sure how to show that it...
  45. Darth Frodo

    LaTeX Sigma tab: LaTeX Reference broken

    Hi guys, when I was trying to post something in the H/W forum and tried to use the Latex reference I could press the tab, but nothing happened. Is this a bug? Thanks!
  46. C

    Are Sigma Algebras Unique for a Given Set?

    Is there only 1 σ-algebra generated for a set? Consider M={1,2}. Ʃ(M)={∅,M} satisfies the definition of a σ-algebra. However, Ʃ(M)={∅,{1},{2},{1,2}} also satisfies the definition of a σ-algebra. However, the way that my text presents these problems (Prove that the σ-algebra generated...)...
  47. C

    Under which circumstances would sigma summation be used instead of integration?

    Just to be clear, I understand the difference between sigma summation and integration. Sigma summation is, put simply, the discrete version of integration. Rather than a continuous sum of a function for given values, sigma summation provides a sum of a function for given regions that is...
  48. T

    What is the issue with the example of \sigma-algebras on infinite sets?

    I am trying to better my understanding of \sigma-algebras, and I have a bit of an issue with one of the examples. This is from Cohn Measure Theory, and before I give the problem, here are two definitions: Let X be an arbitrary set. A collection \delta\Large of subsets of X is an algebra on X...
  49. M

    Understanding Sigma and Sample Sizes - (high Sigma in small samples)

    Please correct me where I am wrong but it seems to me that you could generate a very high value of sigma (e.g. 6 sigma accuracy) from a very small sample size. How then is sigma on its own reliable? Let me see if I understand sigma. To determine the standard deviation I first compute the mean...
  50. W

    Generated Sigma Algebra - Help

    Please help me in understanding Generated Sigma Algebra: Consider S = {(H,H), (H,T), (T,H), (T,T)}, the repeated coin toss. The Sigma-Algebra generated by C = {{(HH), (TT)}} is σ(C) = { ∅ , S, {(HT), (TH)}, {(HH), (TT)} } How does "(H,T), (T,H)" jumped in the σ(C) ? What is the difference...
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