Estimate Definition and 375 Threads

Estimation (or estimating) is the process of finding an estimate, or approximation, which is a value that is usable for some purpose even if input data may be incomplete, uncertain, or unstable. The value is nonetheless usable because it is derived from the best information available. Typically, estimation involves "using the value of a statistic derived from a sample to estimate the value of a corresponding population parameter". The sample provides information that can be projected, through various formal or informal processes, to determine a range most likely to describe the missing information. An estimate that turns out to be incorrect will be an overestimate if the estimate exceeded the actual result, and an underestimate if the estimate fell short of the actual result.

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  1. E

    Optimizing Point Estimates: Bias and Variance Analysis for Mean Estimation

    Homework Statement Suppose that: E(X1) = μ, Var(X1) = 7, E(X2) = μ, Var(X2) = 13, E(X3) = μ, and Var(X3) = 20, and consider the point estimates: μˆ1 = X1/3 + X2/3 + X3/3 μˆ2 = X1/4 + X2/3 + X3/5 μˆ3 = X1/6 + X2/3 + X3/4 + 2 (a) Calculate the bias of each point estimate. Is...
  2. R

    Estimate temperature of Saturn's atmosphere

    Homework Statement To estimate the temperature of the Saturn' atmosphere? (We need to use rotational spectra of CO)Homework Equations B=\frac{h}{8\pi^2 I C} cm^{-1} The Attempt at a Solution I calculated the rotational constant B of CO. I don't know how to proceed further.
  3. 2

    Estimate the number of stars with present-day luminosity function

    Folks, Please don't flame me for this as it is probably already answered somewhere. How does one estimate the number of stars in a 500pc^3 which have a range of 10^-2 to 0.1 Lsun? I am not a maths head, so simple answer that would have the formula would be great. Thanks
  4. U

    Estimate the flow rate and speed of the water going into the turbine

    Homework Statement Run-of-the-river projects harness power from the natural flow and elevation drop of a river. In the Brandywine project, water is diverted from the river into a pipe (r=0.75 m) in which it flows down the hill, through the turbine, and returns to the river. The project at...
  5. mathbalarka

    MHB Hardy & Littlewood's Estimate Result

    Introduction : This thread is dedicated to discuss about Hardy-Littlewood's estimate of the N_0(T), i.e., the number of critical zeros of the Riemann zeta function with imaginary part smaller than T + 1. The final result of Hardy-Littlewood estimate shows that there are infinitely many zeros of...
  6. J

    Estimate the standard reaction Gibbs energy of the following reaction:

    Homework Statement "Estimate the standard reaction Gibbs energy of the following reaction: N2 + 3 H2 ‒‒> 2 NH3 at 100K and at 1000K." Homework Equations ΔS(T2) = S°(T1) + ∫ n Cp dT/T ΔG = ΔH ‒ TΔS Given data: http://imgur.com/MBakUEB (may need to right-click and select...
  7. G

    Estimate exponential distribution parameter

    Homework Statement A certain type of transistor has an exponentially distributed time of operation. After testing 400 transistors, it is observed that after one time unit, only 109 transistors are working. Estimate the expected time of operation. Homework Equations The Attempt...
  8. E

    How do you estimate the sample size of a population given that there i

    i need the formulas and the steps i know how to use the confidence interval equation after that it gets dark $$\frac{N*Var(x)}{(N-1)B^{2}/k^{2} + Var(x)}$$ break down the above equations into many steps and formulas
  9. S

    How to Estimate Optimal Propeller Pitch?

    All, Turning to the experts with a boat problem I'm trying to solve. Specifically, I'm in the process of changing the gear reduction of the transmission on my boat and will need to get a new set of propellers with a different pitch. The old set up worked just ok... I tested different...
  10. D

    Kernal density estimate in polar coordinates.

    Hi, I have a data set containing values for power and direction. I would like to produce a probability density estimate. The data can have multiple sources so I want to use a nonparametric method. I work in python which has a method for kernal density estimation (KDE), which I think should be...
  11. sunrah

    Estimate minimum proton lifetime from internal radiation rate

    Homework Statement Estimate the minimum proton lifetime from the fact that you haven't yet died from internal radiation. Use the following conditions: 1.) At a dosis of Dmax = 2 Greys per year (Jkg-1 yr-1) you would already be dead. 2.) The human body is made mostly of water. 3.) The total...
  12. B

    Why did they choose to estimate the parameter this way.

    Hello, I am taking an introduction class to statistics, in an earlier exam excercise they choose to estimate the answer in an odd way. To make my question concise I will make an abstraction of the problem, and not go into the details, but I can give you them if you'd like aswell. In the...
  13. H

    Common-Source Voltage Gain Estimate

    Homework Statement Working through some homework problems we are given the desired gain and input resistance, and are asked to choose what type of amplifier (mosfet or bjt) and what configuration would be ideal. The solutions are given. In the solutions, and in the design example in the text...
  14. L

    Estimate vs contrast statements clarification

    Hi, I have been reading SAS docs regarding the code for these two, but I cannot seem to really understand the key difference between them, they almost seem interchangeable to me, although obviously they are not. What is the key difference between the contrast and estimate statement and how...
  15. C

    Estimate the fundamental frequency of resonance sound induced by blowi

    Homework Statement Estimate the fundamental frequency of resonance sound induced by blowing on the open end of a half liter bottle Homework Equations f= 1c/4L The Attempt at a Solution i don't know the length of L, what's half liter bottle ..? What does it tell you? 2 x f1?
  16. P

    Find the point estimate of p using method of moments

    Homework Statement Let X1, X2,..., Xn be a random sample of size n from a geometric distribution for which p is the probability of success. Let m denote the sample mean. Use the method of moments to find a point estimate for p. Please write your answer in terms of m. Homework Equations The...
  17. C

    Estimate integral. (Lp Spaces, Holder)

    Homework Statement Show that: \left(\int^{0}_{1}\frac{x^{\frac{1}{2}}dx}{(1-x)^{\frac{1}{3}}}\right)^{3}\leq\frac{8}{5} Homework Equations Holder inequality. The Attempt at a Solution First, I took the cube root of each side. This let me just deal with the 1-norm on the left. Then I...
  18. T

    Quarter Manufacturing Force Estimate

    Hi, What would be the approach to getting a good estimate of the amount of force needed to stamp an American quarter? (This is assuming you have the blank already made) I'd like to get a good estimate, but more importantly an idea of what numbers go into this estimate, i.e yield strength...
  19. L

    Estimate the central temperature of the Sun

    Homework Statement Homework Equations The Attempt at a Solution I'm only stuck on part b). I make a) to be 3.87E26 W, but it gives that anyway in part b). OK, so here's my attempt: \int_{r=0}^{r=R}dT(r)T(r)^3 = -\frac{3L(r)}{16\pi acl_{mfp}}\int_{r=0}^{r=R}dr\frac{1}{r^{2}}...
  20. I

    Use the inverse function theorem to estimate the change in the roots

    Homework Statement Let p(\lambda )=\lambda^3+a_2\lambda^2+a_1\lambda+a_0=(\lambda-x_1)(\lambda-x_2)(\lambda-x_3) be a cubic polynomial in 1 variable \lambda. Use the inverse function theorem to estimate the change in the roots 0<x_1<x_2<x_3 if a=(a_2,a_1,a_0)=(-6,11,-6) and a changes by \Delta...
  21. I

    MHB Use the inverse function theorem to estimate the change in the roots

    Let $p(\lambda )=\lambda^3+a_2\lambda^2+a_1\lambda+a_0=(\lambda-x_1)(\lambda-x_2)(\lambda-x_3)$ be a cubic polynomial in 1 variable $\lambda$. Use the inverse function theorem to estimate the change in the roots $0<x_1<x_2<x_3$ if $a=(a_2,a_1,a_0)=(-6,11,-6)$ and $a$ changes by $\Delta...
  22. T

    Unbiased Slope Estimate in Linear Regression

    Homework Statement There is the suggestion to use an alternative estimate for the slope $$\beta$$ in the linear regression $$y_i=\alpha+\beta x_i+\epsilon_i$$which is formulated as $$B=(y_{max} -y_{min})/(x_{max} - x_{min})$$ Prove that such a formulation of $$B$$ is unbiased. Homework...
  23. A

    MHB How do I find the integral of t^{x-1} e^{-t} from 0 to 1?

    I am reading the red book on special functions of Andrews, and he writes there that: \int_{0}^{1} t^{x-1} e^{-t} dt =\sum_{n=0}^{\infty} \frac{(-1)^n}{(x+n)n!} And I don't see how to arrive at this identity, I guess he expands t in the integrand but my memory is rusty as to this series...
  24. S

    MHB Use differentials to estimate the error

    One side of a right triangle is known to be 20 cm long and the opposite angle is measured as 30°, with a possible error of ±1°. (a) Use differentials to estimate the error in computing the length of the hypotenuse. (Round your answer to two decimal places.) ±...cm(b) What is the percentage...
  25. B

    Expectation of Covariance Estimate

    So I'm trying to take the expectation of the covariance estimate. I'm stuck at this point. I know I have to separate the instances where i=j for the terms of the form E[XiYj], but I'm not quite sure how to in this instance. The answer at the end should be biased, and I'm trying to...
  26. L

    Determining the density of the estimate of the proportion

    Homework Statement In a binomial experiment with number of trials n=1, the probability of success p represents a proportion. The ratio of successes X to the n can be used as an estimator of the proportion. For large n the number of successes in a binomial experiment is normally distributed...
  27. Spinnor

    Estimate of photons/electron/cycle for radio antenna?

    Should it be straightforward to estimate the number of radio wavelength photons emitted per electron per cycle (or is it number of electron cycles per photon) of a half wavelength radio antenna running at 100MHz and 1000 watts power output? Is it many photons per cycle per electron or is it many...
  28. N

    Estimate the number of electrons flowing in a semiconductor pn junction

    Homework Statement The drift current in a p-n junction is 20μA . Estimate the number of electrons crossing a cross section per second in the depletion region. Homework Equations Drift current is the current that occurs due to formation of holes and electrons in the depleted region from...
  29. Z

    How Is a Star's Lifetime Calculated Using Mass-Luminosity Relationship?

    Homework Statement If the exponent, α, in the mass-luminosity relationship is 3.0, estimate the lifetime of the above star. (You can assume that the Sun’s lifetime is 1 x 10^10 years). Homework Equations L*/Lsun = (M*/Msun)^α lifetime ∝ M/L ∝ M^-2 The Attempt at a Solution...
  30. Ackbach

    Rough OoM Estimate for Number of HW Problems Assigned

    I'm just starting out teaching in a US high school, and I have AP Physics B that I'm taking over in the Spring. I've never taught physics before except in a tutoring context. All my students are seniors, and are taking 7 classes total! Each of those classes meets 4 times per week. So I can't...
  31. Telemachus

    Estimate molarity from enthelpy, gibbs energy and entropy of formation

    Hi there, I have to solve this problem: Use the following data to estimate the molarity of a saturated aqueous solution of ##Sr(IO_3)_2## So, I think I should use the Van't Hoff equation in some way, but I don't know how. I also have: ##\Delta_r G=\Delta G^o+RT\ln K## ##K## is the...
  32. S

    Estimate p from sample of two Binomially Distributions

    1. Suppose X~B(5,p) and Y~(7,p) independent of X. Sampling once from each population gives x=3,y=5. What is the best (minimum-variance unbiased) estimate of p? Homework Equations P(X=x)=\binom{n}{x}p^x(1-p)^{n-x}The Attempt at a Solution My idea is that Maximum Likelihood estimators are...
  33. C

    Maclaurin remainder interval estimate

    Homework Statement The question asks to estimate the remainder on the interval |x|≤ 1. f(x) is given as sinh(x). I solved the polynomial P3(x) = x + (1/6)(x3) I then went ahead and solved R3(x) up to the point shown below. R3(x) = (sinh(c)*x4)(1/24)I then don't know how to go about...
  34. C

    Point estimate from multiple sampling distributions

    Dear all, I hope someone can help me. I have two experimental groups, A (n=5) and B (n=8) containing biological samples. The samples are used to estimate my parameter of interest, θ. I do this with Markov-chain Monte-Carlo, which gives me a posterior distribution of θ for each of my samples...
  35. A

    Estimate decoherence time and length?

    what is the formula for estimate decoherence time and decoherence length from voltage, current and resistivity value ?
  36. D

    Archived Estimate nuclear energy generation rate (formula given) per unit MASS MASS?

    Homework Statement Consider energy generation in the Sun. Fusion through the pp cycle takes place within its core which has r = 0.2 Rs T = 1.3 x 10 ^ 7 K rho (density) = 1.1 x 10 ^ 5 kg m^-3 X (total mass fraction of hydrogen) = 0.34 The nuclear energy generation rate for the pp...
  37. R

    Webpage title: Estimating the Diameter of the Moon Using a Total Solar Eclipse

    Assume that the average distance of the sun from the Earth is 400 times the average distance of the moon from the earth. Now consider a total eclipse of the sun and state conclusions that can be drawn about: A. The relation between the sun's diameter and the moon's diameter. B. The relative...
  38. E

    Use linear interpolation to estimate sin 36 using as your 'known' values 0 & 60?

    here is the answer: 36/60 = x/.8660 60x = .8660 x 36 60x = 31.176 x = .5196 however, where does the value: 0.8660 initially come from? any help would be appreciated
  39. S

    Estimate the Hydrogren Burning Lifetimes of Stars

    Homework Statement Estimate the hydrogen burning lifetimes of stars on the lower and upper ends of the main sequence. Lower end: M = 0.085 solar masses; log10(Teff/K) = 3.438; log10(L/Lsolar) = -3.279 Upper end: M = 90 solar masses; log10(Teff/K) = 4.722; log10(L/Lsolar) = 6.045...
  40. B

    Use differentials to estimate the change in tension of yo-yo string

    . Homework Statement The tension T in the string of the yo-yo is given by: T=(mgR)/(2r^2+R^2) where m is the mass of the yo-yo and g is the acceleration due to gravity. Use differentials to estimate the change in tension if R is increased from 3cm to 3.1cm and r is increased from 0.7cm...
  41. P

    Make a rough estimate of the volume of your body (in cm3).

    Make a rough estimate of the volume of your body (in cm3). 8X10^5 cm^3 8X10^3 cm^3 5X10^4 cm^3 5X10^3 cm^3 8X10^4 cm^3 How to solve this problem?
  42. J

    How to transfer designed capacity to estimate production ?

    Hi, Today I was reading news about Poland investing into nuclear energy where they estimate the first reactor to start generating in 2023 with capacity of 3MWe. How can we estimate yearly production of the actual output send to the customer ? (I'm more into PV technology but I think...
  43. A

    How to estimate tangential force through curve?

    Homework Statement A capsule suspended on flat rails enters a curve in a pipeline. It has guide wheels on vertical axles to keep the main wheels on-track. As it enters the bend the front guide wheel impacts the side of a rail to steer the bogie. What is the force of this impact? Essentially...
  44. R

    How to estimate return period amount at different distributions

    I have yearly rain amounts and want to estimate the rain with 100 year return period assuming different distribution. I know some ways to do with for example normal dist. but it's not general for all pdfs.
  45. H

    MHB How Can You Determine the Sum of an Infinite Geometric Series?

    i.e. \sum_{n = 0}^{\infty}\frac{1}{2^{n}} = \frac{1}{2^{0}} + \frac{1}{2^{1}} + \frac{1}{2^{2}} + \frac{1}{2^{3}} + \frac{1}{2^{4}} + \frac{1}{2^{5}} + \frac{1}{2^{6}} + \cdots = ~1.99138889... Is there a way you can know this solution is 2 without having to perform all of the calculations I...
  46. C

    How Many Groups Exist with Order 24?

    how would you estimate number of groups of order 24? i do not need exact number, it is 15. I know that there are 5 groups of order 8 and there is 1 , 4 or maybe 7 sylow 3-groups. but i do not know what to do next
  47. S

    Estimate the lifetime of the excited state that produced this line.

    Homework Statement An atomic spectrum contains a line with a wavelength centered at 460 nm. Careful measurements show the line is really spread out between 459 and 461 nm. Estimate the lifetime of the excited state that produced this line. Homework Equations Change in Frequency =...
  48. E

    Use the density of the liquid to estimate the radius of a neon atom.

    Homework Statement Neon is a monatomic gas; Density = 0.900 kg.m-3 Pressure = 1 atm Temperature = 273K. Density of liquid neon = 1207 kg.m-3 (i) Calculate the volume occupied by one gram mole of neon at a temperature of 273 K and a pressure of 1 atm. (ii) Determine the atomic...
  49. L

    Estimate a number within two (or more) overlapping ranges of number

    Hi everyone, Let's say a simulation outputs a range of estimates with various accuracy level, ranging from 30% to 100%, with the range given at 30% being widest and the range at 100% being the narrowest. The ultimate goal of this simulation is to arrive at a single number within the estimated...
  50. A

    Edvard Munch's "Scream" Up For Auction: 80M Estimate!

    "Scream" on sale! Yes, THE "Scream", by Edvard Munch is now to be auctioned at Sotheby's. Munch made 3 (I believe) versions of this painting. This picture has been in private ownership by the shipping family that supported Munch financially (the Olsen family). Now, Petter Olsen has...
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