# sigma

2. ### Help with a proof

Hey guys. I found out that a Î£2n n=1 EQUALS [a^2 - a] However, although I can see that it works, I can't figure out why this is true. Can anyone figure this out?
3. ### How Can I Represent These Progressions in Sigma Notation?

I would like to represent the following finite progressions in sigma notation: 1. Finding the $n^\text{th}$ term of a geometric progression: $a_n=a_1(r^{n-1})$, where $a_1$ is the first time and $r$ is the common ratio 2. The sum of a geometric progression: $S_n=a_1\frac{1-r^n}{1-r}$ 3...
4. ### Show the the intersection of two sigma fields is a sigma field

In probability, a sigma field (algebra) is defined as a set F whose elements are sets and that satisfies the following properties: 1. The null set and the sample space are members of F. 2. If an event A is a member of F, then the complement of A is a member of F 3. If events A1, A2, â€¦ An...
5. ### Double sigma

I am reading my Bulgarian textbook about Electromagnetism theory. I found an expression, which I can't understand. Here I attached the expression to my post. Please, help me to understand this "double" sum from pure mathematical point of view. What does the expression mean? I will be very...
6. ### Sigma rule question

Hi everyone I was wondering why this equality is true considering that $d_i$ is not a constant $\sum E(d_{i}u_{i})=\sum d_{i}E(u_{i})$ $$d_{i}=(x_{i}-\bar{x})$$ Thank you in advance
7. ### All N samples within one sigma

If I have a random variable which has a normal distribution with mu and sigma, what is the probability that if I draw N samples that they are all less than one sigma away from each other? I am not having any luck coming up with how to calculate this answer. I did write a program to try to...
8. ### Probability - Sigma algebra

I read in a book "The elements of sigma - algebra over a sample space omega are called events" and not all subsets of a sample space are events. Can you please explain this definition?
9. ### Simplifying Steps in Summations (SIGMA)

Hey guys, I am new to the forum as you might possibly see on my post count :cool: I am currently studying "The Art of Computer Programming" by Donald E. Knuth. There is quite a strong section on number theory and I really try to understand what he says and to solve the exercises he is giving...
10. ### How to solve: How can I solve: âˆ‘{k=1,n} [k^2Â· k^(-1)]

Solve: âˆ‘{k=1,n} [k^2Â· 2^(-k)]
11. ### Summatory (Sigma) properties

Hello, I can not find the way to solve the following equation: sum of k^2 f(k) from k=1 to n. In Particular, k^2 * 1/k
12. ### Sigma

What does the sigma mean in this formula for finding the mean of grouped data? x=Î£fx/Î£f
13. ### Analytical solution to consecutive inner sigma notations

Hey! Does anyone know if there is any way to solve the equation in the image analytically? I have been working with this for some time now and cannot seem to get past this version of the equation :/ It is the probability to complete a game of memory in round (n/2 + N, n=amount of cards...
14. ### By integrating show that EX = muu and DX = sigma

How would you show by integrating that EX= \mu \; and\; DX=\sigma^2 (with out making it impossibly difficult to follow/understand) \frac{1}{\sigma\sqrt{2\pi}}\,e^{ -\frac{(x-\mu)^2}{2\sigma^2} }
15. ### Can This Be Written In Sigma Notation?

I don't know if I should call this a sequence or a series or what but here are the terms: 1 Previous term + 1 + 2 = 4 Previous term + 1 + 2 + 3 = 10 Previous term + 1 + 2 + 3 + 4 = 20 and so on Can it be written in sigma notation? Is there a quick way to find the 20th term, 50th term...
16. ### What means sigma of the laplace transform?

The kernel of the laplace transform is exp(-st) = exp(-(Ïƒ+iÏ‰)t). I know that dÎ¸/dt = Ï‰, but what is Ïƒ in terms of others physical/mathematical quantities already known?
17. ### Challenging Sigma Problem

This problem was on a teacher's exam. Please help to solve, explaining all steps. http://web.mail.comcast.net/service/hom ... 262&part=2
18. ### Statistics Sigma problems

Hello, first time taking stats and i just want to make sure my answer make sense. given this table of values person(i) Xi Yi 1 6 9 2 4 5 3 6 3 4 0 7 5 7 8 5 ...
19. ### Derivation of tau function, sigma, euler and mobius function

I am interested in deriving the formula of four number theoretic functions.To those who will get to see these, kindly check my work (attached pdf) and do comment on them. Your opinions and suggestions are greatly appreciated. There will be more future posts about number theoretic functions and...
20. ### Series, Sequences, Sigma Notation

I need help with this: I have to write this sequence in sigma notation: 4,11,30,67,128 Please help quickly!