Applied Mathematics

250-300 tests are conducted with two (A, B) coins. The second B (ideal) coin is introduced due to the possibility of dishonesty of the first coin. The coincidence / mismatch of the symbols ("common game") is tracked. After the completion of 1 test cycle, 2, 3, etc. (between cycles 1000 tests of coin A) are carried out. Previous cycles are forgotten. I draw a graph: match (move point up from axis 0), mismatch (move point down from axis 0). We obtain a random walk. How to calculate the maximum deviation of a point from zero on a particular step? earlier I determined the standard deviation (1-sigma, 2-sigma, 3-sigma) √npq. then I learned about the mathematical ex…

The famous game-theoretic couple, Alice & Bob, live in the set-theoretic universe, VV, a model of ZFCZFC. Just like many other couples they sometimes argue over a statement, σσ, expressible in the language of set theory. (One may think of σσ as a family condition/decision in the real life, say having kids or living in a certain city, etc.) Alice wants σσ to be true in the world that they live but Bob doesn't. In such cases, each of them tries to manipulate the sequence of the events in such a way that makes their desired condition true in the ultimate situation. Consequently, a game of forcing iteration emerges between them as follows: Alice starts by forcin…

What does (x-a)(x-b)(x-c)...(x-z) equal to? Solution :

This is the upgrading of my first research with the same subject, which can be found in https://www.linkedin.com/pulse/relationships-between-prime-number-fibonacci-thinh-nghiem/?lipi=urn%3Ali%3Apage%3Ad_flagship3_profile_view_base_post_details%3BCuXz0krLTjSmIWUuweQOBg%3D%3D My conclusion in the first article has been optimized as below: A whole number, odd or even, can be analyzed as the sum of a prime number and two Fibonacci numbers. Here we have some examples 52362 = 52127 (prime) + 2 (Fibonacci 1) + 233 (Fibonacci 2) 52381 = 51769 (prime) + 2 (Fibonacci 1) + 610 (Fibonacci 2) Also, this time I verified with range [5 - 10,000,000 (ten mill…

Prime ={NPn*±IPn } i.e 30N±I5, Prime Number range 5<=P<25, I5 have 2 AP series with C.D=6, and first element = 5 & 7 5,11,17,23….infinite, C.D=6, T1=5 7,13,19,25…..infinite, C.D=6, T1=7 in example below you can see with help of I5 AP series we can find all Prime Number range 5<=P<25 P5* I5 I5 Prime=(P5*-I5) Prime= (I5-P5*) 30 25 35 5 5 30 2…

Hello! I have developed the PDF (probability density function) of a new distribution. I want to calculate their moments (mean, sd, skewness, kurtosis). How can I do this? Consuli

How is the best way to prove that a SPD problem is a dual of other SDP problem? I have a SDP problem primal and its dual. I know that they are dual and primal. But how I can prove it mathematically?

We are getting ready to build a house and are going to place solar panels on our roof. Would a 25-30 foot difference in height (with the same angle) affect the amount of sunlight that the panels would get in a substantial amount?

Can anyone solve or help me find solutions for: x + z - y = (0 or 15) with x, y, and z ranging between 0 - 15?

Very average maths here. Rusty on Excel, once fairly competent. I am trying to construct a simple chart in excel Here is the data: Age of the Earth 4.54 (billion years) Archean Era begins 3.8 Proterozoic begins 2.5 Phanerozoic begins 0.57 I am looking to create a sunburst or donut type chart where it shows the eons in segments. 4.54 would be 360 degrees of the chart. I term this whole life of the planet" here "whole" The other numbers would have to be calculated as percentages of the whole I have two questions please: 1] Which formula can you use to express 4.54 as 100% (not as a fraction of 100% but AS 100% or …

Couldn't find economics sub forum so I'll put it here instead. So, if you want to buy or sell a share on a share market you would normally have to pay a premium to a broker who would make the sale on your behalf. Is there any general rule as to how long it takes for the combined cost of premiums to exceed the price of the share itself? I guess, it's a bit vague since the price of the share is not constant, but so are the premiums... Not considering derivatives like options and such for the sake of this question.

Hi, I writing one article about entropy functions and I have a problem. I was searching a many books with this subjects and I was not find anything. In my text I am talking about entropy functions like marginal , conditionally, marginal, relative, cross entropy and Burg, Jeffreyes, Jensen-Shannon, Renyi and Hartley entropy. I need this calculated entropy functions and graphics on one example and make a conclusion on applicability certain entropy function on that example. Please help, and thanks in advance.

Hello everyone. I've got another probability puzzle that I actually did solve, but I feel like I may have taken a longer route than necessary to arrive at the solution. I'm wondering if there is a simpler, more elegant way to solve it than the "backwards" approach I took. Basically, the problem is that you have 40 cards remaining in a deck, with all four aces still in the deck. If you draw two cards, what is the probability that exactly one card will be an ace? I didn't know how to solve it directly, so I thought it would be easier to find the probability of *both* cards being an ace and the probability of *neither* card being an ace, and subtract those amounts …

Hello everyone. I downloaded a puzzle app from the Play Store that has probability puzzles, and I hate to admit I'm already stuck on the second puzzle! But I feel like I'm doing it correctly, though it says my answer is incorrect. I'm just looking for some general guidance for if I'm on the right track. I don't want the answer or a direct solution. If I'm wrong, a suggestion for certain keywords I could search for and read up on would be helpful too. Here is the puzzle: First off, I'm wondering if the word "uniformly" means something that I'm not aware of. I've never studied probability, so perhaps that's one aspect I'm missing. Second, even though it seems l…

What is wolfram alpha saying here, where ... = that equation. Like this was the solution given by wolfram alpha to this for a physical object, which is literally impossible that ... = that. Where the closest definition I could get for ... was Morse code for S or Forever in like summation notation, where F = I = Moment of Interia as it kept taking I for i but that doesn't matter in this context, where I got this twice, no matter how it took I, the Azimuthal angle transformation is cut off in the second picture but was the same. Where either this solves infinity or explain.

Hi, Ive recently worked on a chemistry question which required a volume conversion from cm^3 to m^3 Specifically the number was 10 cm^3 and it shouldn't have been as difficult as its ended up being, but i eventually got the right answer. However, the method which gave the right number, was in the format of: (10 cm^3 / 1) * (...m^3 / ...cm^3) = 0.00001, of which turned out from (10 cm^3 / 1) * (0.001 m^3 / 1000cm^3), which seems to give the right conversion factor. This was worked out from equating them as follows: 10 cm^3 = 0.1 m^3 ... then, (10)^3 cm^3 = (0.1)^3 m^3 ... which gives 1000 cm^3 = 0.001 m^3, and then using those values in the equation (…

Hi all I have a question concerning detecting outliers in small samples. My results are: 14.1, 4.1, 8.1, 9.1, 8.2, 8.6 - i suspect outliers are 14.1 and 4.1 Which statistical test should i use to analyze this data? I thought about Extreme studentized deviate test but it turned out to be used for big sample sizes. Thank you so much in advance ^^

The sides of a parallelogram are 4cm and 6cm, and the angle between the sides is 30 degree. Find the area of the parallelogram. (without the use of trigonometry or vector; this is for a 8th std student)

Hello Everyone, I regularly use linear and nonlinear regression. However, I realized recently that I don't know much about confidence intervals. After consulting several books and the ProStat manual, I found myself stuck on why ProStat calculates two values for the 95% confidence values. One is "Uninvariant," and the other is "supporting plane." The supporting plane limits are greater than the uninvariant ones in the examples from the manual. The manual says that when something called k = p (the number of parameters) we get the support plane CI's, and when k = 1, we get the uninvariant CI's. It is unclear from my reading of the manual what k is. The manual prov…

So, I was thinking about the Lascaux cave and how much I wanted to see it. I know it's locked up but there is a 3 d model somewhere. Then I started thinking that one could share this vision using virtual reality. I confess I don't know much about this subject but simply putting a fixed point 3d map from one single location did not seem enough. Then I started imagining a drone flying through the cave mapping with a camera. As the drone flew through the space, there would be a grid so that it's image would be located into the three dimensional space. As the drone flew more and more, the space with gain further detail. At any given point in time, the drone would 'see' only …

Hi, Is there anybody can help me solve the problem below? I now have a function f(t) = 1/(p(t)+1) * dp(t)/dx. How can I convert this into Laplace domain. Thanks.

Hello, Suppose there's a circle with radius r and centre C. Let there be a point outside the circle P, such that the length PC is known. Now, lets take a point X on the circumference of the circle, such that the inclination of CX with respect to PC is a. Is it possible to find PX? If so, how??

The SIR model is 3 EDO's I am looking to estimate the parameters (b, y) with the method of Gauss Newton The real data they give me are only the number of infected from day 1 to 14 The system lacks analytical solution I solve with Euler this gives me the numerical approximation of the system, Approach the problem of initial values ​​with Cauchy (DS / dt) = -s * i * b (DI / dt) = -s * i * b - y * i (DR / dt) = y * i Where S: susceptible persons I: Infected people A: People removed The problem is that when estimating the partial derivatives, I do not understand from which equation to estimate them since it seems logical that I can not do it from dI /…

I know there is a proof that angles can not be TRISECTED,but does it really mean we should give up the search for any possible method? Below is a TRISECTION procedure(I ever sent to a Board of Discussion ). And I need the comments of this Board's members:either in FAVOUR or AGAINST with REASONS: I need to reserve the calculations involved in the proof of the Trisection Procedure and go straight to an Undisputable(Practical) proof: It is not by chance/guess that an(y) angle can be TRISECTED ; but has a Concrete Proof from a familiar but hidden Rule/Law I have Discovered which Scientists/Mathematecians have failed to Notice/Apply since the Dawn of maths to Trisect…

Dears, Recently when learning programming language, I accidentally found out an interesting relationship between prime number and Fibonacci number. That is, a positive integer number can be analyzed as either - the sum of a prime number and a Fibonacci number For example 16 = 11 (prime) + 5 (Fibonnaci) 61 = 59 (prime) + 2 (Fibonacci) - or a prime number minus a Fibonacci number For example 59 = 61 (prime) – 2 (Fibonacci) 83 = 227 (prime) – 144 (Fibonacci) I have tried with the first 1,000 positive integer number from 1 to 1,000 MANUALLY and ensured that all of them matched with one of the two above rules. I shared my analyzing here …