Estimation Definition and 181 Threads

Problem: Relatively low mass stars can be shown to have their radii dependent on their mass as; R\proptoM1/2 From this, show that the temperature in kelvin at the centre of such a star can be estimated to be \approx24\times106(M/Msolar)1/2 Relevant Equations...

Hello there, currently I am trying to solve a least squares problem of the following form: min_{M} ||Y - M*X||^2 where M is a 3x3 matrix and Y and X are 3xN matrices. However, the matrix M is of a special form. It is a rank 1 matrix which satisfies M*M = 0_{3x3} and the trace of M is zero...

Homework Statement (x1,x2,...xn) is modeled as observed values of independent random variables X1,X2,...Xn each with the distribution 1/θ for x in [0,θ] and 0 otherwise. A proposed estimate of θ is m = max(x1,...xn) Calculate the distribution of the random variable M=max(X1,X2,...Xn) and...

Hey, there's this thing I can't wrap my head around. Let's say we have a negative binomial variable x, with parameters p and r. That is, x is the number of failures we get before the rth sucess, while looking at random bernolli variables with sucsess rate p. It can be shown that...

Dear all, One of the main challenges in social science is inferring causality from nonexperimental data. Statistics can help. In a regression context regressing Y on T may not give the causal effect of T on Y due to unobserved confounding. A solution is finding a variable Z, called an...

I don't understand this estimation lemma example :( We are given the 'curve', And part of the example is showing that the contour integral over the top semicircle C_R tends to zero. Apparently we use the estimation lemma and the fact that, |z^2 +1| \geq |z|^2 - 1 to show, \left|...

hi all, i would appreciate any help you can offer for the following problem. consider coordinates x_1, x_2 in the plane for which ||x_1-x_2||=d. suppose that this pair of coordinates can be measured independently, and that the measurements are 2D normally distributed with means x_1, x_2 and...

Hi All I recently purchased a 1000w heating element for coffee cups, http://www.ebay.com.au/itm/110668421004 that I will be using on a 240v AC source. I would like to know if a cup out of silicone will withstand direct contact with the element? From what I am reading normal silicone...

I'm working on doing some parameter identification for a small UAV model, but unfortunately due to the size of the aircraft, we are unable to measure alpha and beta directly. What we do have are X/Y/Z position and acceleration, velocity, roll/pitch/yaw angles, and roll/pitch/yaw rates. Is...

I am using LG Optimus 2x smartphone(Gyroscope and Accelerometer sensor) for positioning. I want to get correct rotation angles from gyroscope that can be used later on for body to Earth coordinate transformation. My question is that 1- How I can measure and remove the drift in gyro sensor. The...

Hello, Would anyone be-able to recommend a good, easy to read article which outlines MMSE and its derivation. Specifically I am having trouble finding this term + \int x'xP(x|y)dx-\left \| \int xP(x|y)dx \right \|^2 from E({\left | \left | X-z \right | \right |}^2|Y=y)...

Homework Statement If y''=-y^2, is this approximationg an over-estimation or an underestimation of the exact area? Homework Equations The Attempt at a Solution

I am trying to do a finite element analysis ofcold extrusion process of a tube wherein the steel tube is reduced from a larger outer diamter to a smaller one by extrusion process.The tube is held stationary and the die is pushed into the tube for a particular length and then retrieved.I am...

I am working on a project involving this setup (please refer to the pic). Basically compressed air at a constant flow rate flows through a 1/4" tube to the tube shown and gets heated by the star-wound heater and, this hot air heats the small inner vessel and then leaves the system. Now I am...

hi everyone, i would be grateful for suggestions for the following problem: i have a set of measurements, discrete samples from a continuous function of time. with each measurement comes a estimate of its uncertainty (standard error). by doing a discrete Fourier transform, i have seen some...

Hi I have a problem to solve and I'm stack, so I would really appreciate your help if anyone can tell me how to answer the following question: "Consider a sky imaging system that has a 100m wide FoV measured at 1km from the camera; and that images a passenger airliner at a height of 2km as 10...

Hi, I have a set of data. What I want to do is say with a 95% certainty this is a positive trend, or it is a negative trend. Basically I have a set of observations (X_i, Y_i) where i is in {1,2,3,4,5,6...} and X_i = i and Y_i is an observation. Right now I have the Variance, the...

Hello everybody! Since some time I am trying the estimate the density of a set of numbers (in my case the numbers are distances to some object from a laser scanner). As I read, that the kernel density estimation technique is a basic approach for that kind of problem. Different Kernels can...

Hi all, What is a good way to use replication methods for estimation? For a dataset with no design information, only weighting remain. I know the basic principles of replication. Are there any considerations to use replication effectively? There is a public data of 15,000 people from the...

1. Jean camps beside a wide river and wonders how wide it is. She spots a large rock on the bank directly across from her. She then walks upstream until she judges that the angle between her and the rock, which she can still see clearly, is now at an angle of 30 downstream (as shown in the...

Hi, I am not sure if this is the right forum to post this. I am working on a Kalman Filter for battery state of discharge estimation during discharging process. I am using a Linearized Discrete Time Kalman Filter to estimate the State of Discharge/SOD (how much % of charge has been taken...

Dear All, What is the best approach to estimating energy from incinerator waste heat? Note that it is medical waste being incinerated. Thank you so much.

Hi, I need to calculate an estimate of the reflected electron beam power in the form of back scattered electrons and secondary electron emissions from a tungsten/Graphite target. The Electron source is a 25kV source with operated at a power of around 25kW. The tungsten. graphite blocks are...

Problem is solved. :)

Homework Statement It seems that I'm a little bit lost about this exercise. It says: Find the taylors polynomial of third degree centered at the origin for z=\cos y \sin x. Estimate the error for: \Delta x=-0.15,\Delta y=0.2. So, I did the first part (the easy one), the taylors polynomial for...

Ok this kind of question seems to come up a lot in research and applications but has me completely stumped. Say we have a dynamical system x_{t+1} = Ax_t where for simplicity we'll assume A is a constant symmetric real matrix but otherwise unknown. 1. What is the "best" estimate of A, when...

I don’t know if this one is the appropriate forum for the following question. If for this question it is better another section of the forum, point out to me, please. I know the global radiation on a south oriented surface, in a German locality. Do you know methods to estimate the direct...

Homework Statement Minimal growth medium for bacteria such as E. coli includes various salts with characteristic concentrations of mM and carbon source. This carbon source is typically glucose and it is used at 0.2% ( a concentration of 0.2g/100mL). a) Make an estimate of the number of...

can we estimate effective masses of electron and hole from the band structure if yes how? can somebody explain with reference to Si band structure?

Homework Statement "Estimate the mass of water in all the World’s oceans." Homework Equations I know the following: Two-thirds of the Earth is sea. The density of seawater is 1025 kg/m3. Radius of the Earth = 6.3*106m. The Attempt at a Solution Let's assume that the...

Homework Statement This is a problem in numerical estimation. Estimate a typical maximum momentum pmax for the free electrons in a metal where pmax = \left(\frac{3nh^{3}}{8\pi}\right)^{1/3} (In estimating n, the number density of free electrons, assume there is one such electron...

1. Homework Statement The small scale drawing given in the Annexure shows the general arrangement and dimensional data on an early version of the English Electric “Canberra” B.1 bomber, powered by two Rolls Royce “Avon” jet engines. It was and is an extremely successful aircraft, designed by W...

Homework Statement The small scale drawing given in the Annexure shows the general arrangement and dimensional data on an early version of the English Electric “Canberra” B.1 bomber, powered by two Rolls Royce “Avon” jet engines. It was and is an extremely successful aircraft, designed by W E...

Hello, I use Arnoldi iterative algorithm in order to compute the eigenvalues of a matrix. I know that the eigenvalues are of the form \lambda(1+j/c) and I can totally estimate them. The problem that occurs is that both the range of \lambda_0 and c is for example [100,1000]. That means that there...

Hello everybody, I hope I am posting this under right topic. I am running a research project and we are recording videos of subjects from both frontal (back) and saggital (side) plane while they are walking on the treadmill. I put 10cm long calibration marker on the back of the subject. This...

hi all, the situation is this: i have a conditional PDF f_{X|(D,S)}(x|d,s) and the unconditional PDFs D and S, f_{D}, f_{S}. Now, I can marginalize the joint PDF f_{X,D,S}=f_{X|(D,S)}f_{D}f_{S} by integrating over d and s over their respective supports. What I'm really interested in is a...

I got a question on estimation theory. Can anyone explain it to me or give me a link with some tut and solutions so I can get a better understanding. I got a maths question which i have asked for help but no one has replied yet. Since it was a statistical question I should have posted it...

Hello everyone, I just started reading "Fundamentals of Statistical Signal processing" by Steven Kay and just got done with the first chapter, which describes the estimation problem, PDFs etc. It has some very interesting problems at the end and some of them have me a bit confused. I think...

Hi, 1- Please explain conditional & unconditional mean square error, and their difference. 2- Which one is the solution for minimum MSE estimation? (that is conditional expectation: E \left[ X|Y \right] . I meant which one is minimized by selecting the conditional expectation.) 3- What is...

I've been playing around with a forumlaic representation of a known square roots estimation method and I came up with this: This estimation has several interesting properties to it which I've been looking into. My main concern is the fact that I'm using SQRT(x) in the equation which...

Homework Statement \Sigma(-1)^{n+1}\frac{1}{n!} How many terms will suffice to get an approximation within 0.0005 of the actual sum? Find that approximation. Homework Equations No idea.The Attempt at a Solution What I tried doing is setting my absolute value of the series less than 0.005, but...

Does anyone know how to calculate the mass of compressed hydrogen tank at certain pressure. The tank is cylindrical with hemispherical ends. I have pressure,radius,wall thickness and length,internal volume and density of the material. The tank is a Type IV tank.(Composite tank with...

Homework Statement Find the error estimation for the integral \int(1+x^2)^\frac{1}{4} with limits [0, 2] for n=8. Homework Equations \epsilon\leq \frac{|f^{(4)}_{max}(x)|(b-a)^5}{180n^4} The Attempt at a Solution The tricky part about this problem is finding f^{(4)}_{max}(x)...

Homework Statement Estimate to 1 significant figure the total # of air molecules in this room (l=20ft, w=14ft, H= 8ft) Find molecules/room Homework Equations 1 mole = 22.4 liters 6.02 x 10^23 molecules = 1 mole The Attempt at a Solution volume of room = 2240 ft^3 or approx 683...

I am wondering if Kernel Density Estimation (KDE) is appropriate for some data analysis I'm working on. I have a simulated process that produces a large number N of pieces of debris, and I want to know how these objects are distributed spatially. In other words, I'd like to estimate a density...

I have 2 problems I am currently stuck on.. one being In a large sample study according to a report by the U.S. surgeon general, electrical engineers have the lowest smoking rate among all workers surveyed. Only 16% of the male electrical engineers in the sample smoke cigarettes regularly. How...

Homework Statement i did a lab on determination of refractive index of an opaque dielectric material, using the brewster angle. We took a couple of readings on a spectrometer at the position of complete extinction, now how do i get the error estimate ? The angles were taken to the nearest...

Homework Statement The problem from the book states The problem I am having is actually trying to figure out how someone else's suggested solution. His idea was to take a value R for the mean radius of the sun: R=6.96x10^{5} km And use trig to find out a rough distance. Homework...

Homework Statement f(x;theta)=Exp(-x+theta) Find parameter estimates for variable 'theta' using maximum likelihood Estimator and Method of Moments. Homework Equations Log(x; theta) = Log(Exp(-x + theta)) -- For MLE Integral from theta to infinity of (x*Exp(-x + theta)) = xbar -- For Method of...

This should be a fairly easy problem, although my Heat Transfer is quite rusty. I'm trying to get a ballpark estimate for a rotating cylinder that has flow on both the inside and outside. I know the temperature of the air at the inlet and outlet and am trying to get a decent estimation for...