Variance Definition and 357 Threads

  1. D

    Calculating variance from range

    Hello, I have taken 5 samples and found that my average concentration is 5 mg, with a range of .003 mg in either direction. I would like to calculate the variance with only this information. Is this possible? I am used to calculating the variance from the standard deviation, but I don't...
  2. R

    Me the variance of the score function in exponential distribution

    please help me! the variance of the score function in exponential distribution Homework Statement My question is about exponential function, with its density function known as f(x;theta) = (1/theta) e^(-x/theta) for all x>0. where E(x) = theta, var(x) = theta^2 My question is, what...
  3. R

    Me the variance of the score function?

    please help me! the variance of the score function?? I have been stuck with this one particular question over this weekend, and unluckily I could not figure it out by myself. If you can help me a bit with this problem, I will really really appreciate it. My question is about an exponential...
  4. C

    Why is the variance of the Parzen density estimator infinite?

    Hello everyone, I'm new to this forum and I'm glad to have found such a high quality resource where we can have such valuable guidance and discussions. I've read somewhere that the variance of [tex]p(x) = {\frac{1}{n}}\sum_{i=1}^{n}\delta(x-x_i) \forall x \in \Re[\tex], in which [tex]D_n =...
  5. P

    Find mean and variance of X and Y

    Homework Statement I have found the marginal distribution for X and Y from a table. (No statistical regression, just simple table) How should I proceed in finding mean, variance an correlation coefficient of X and y? I am computing by hand. Thank you, Homework Equations The...
  6. T

    Prove the sample variance formula.

    Homework Statement Prove that the sample variance of a sample is given by S2 = \frac{\sum^{n}_{j=1}x_j^2 - \frac{1}{n} (\sum^{n}_{j=1}x_j)^2}{n-1} Homework Equations N/A The Attempt at a Solution For my purposes it is sufficient to show that: \sum^{n}_{j=1}(x_j -x_j^2) =...
  7. T

    Find the Variance of this distribution

    Homework Statement The number of hours spent in a library per week by arts and science students in a college is normally distributed with mean 12 hours and standard deviation 5 hours for arts students and mean 15 hours and standard deviation 4 hours for science students. A random sample of...
  8. D

    Proving Variance of t Distribution

    How to prove the variance of the t distribution?
  9. G

    Bernoulli Variance: Calculating Var[Xi] as a Function of p

    Homework Statement Show how Var(Xi) depends on p writing it as a function \sigma^2(p) The Attempt at a Solution Var[Xi] = E[Xi^2] - E^2[Xi] = p-p^2 = p(1-p) not sure where to go from here to get it in the form \sigma^2(p) ?
  10. J

    Calculating Mean and Variance of a Normal Distribution

    Please try this question and see whether you got my answer...i am having some doubt The random variable X is normally distributed with mean V and variance C^2. It is known that P(x>102)=0.42 and P(x<97)=0.25 calculate V(mean) and variance c^2 i got mean 100.8 and variance(-5.7)^2
  11. G

    Variance of Linear combination of random variable

    This is a problem from my A levels Stats2 book. I understood the problem but one of my answers doesn't seem to be correct according to the book so I thought I better be sure! Homework Statement A piece of laminated plywood consists of 3 pieces of wood of type A and 2 pieces of type B. The...
  12. K

    What is the integral method for finding the mean in exponential distribution?

    in the exponential distribution we know that μ = 1/λ and σ = 1/λ^2 also f(x) = λ*e^-λχ how can i find the mean (μ) using integrals? generally what we do is this we integrate from a point to another the x*f(x) (EX) And the variance is EX^2-(EX)^2 but here we have no points...
  13. O

    Distribution arising from randomly distributed mean and variance

    forgive for my ignorance, but i have a practical problem that i don't know how to approach: X\sim\mathcal{N}(\mu,\sigma^2) where \mu\sim\mathcal{N}(\mu_{\mu},\sigma_{\mu}^2) and \sigma\sim\mathcal{N}(\mu_{\sigma},\sigma_{\sigma}^2) what is the resulting distribution of X, in terms of...
  14. N

    Taylor expansion of gaussian integral with respect to variance

    Hi everyone. The problem I have to face is to perform a taylor series expansion of the integral \int_{-\infty}^{\infty}\frac{e^{-\sum_{i}\frac{x_{i}^{2}}{2\epsilon}}}{\sqrt{2\pi\epsilon}^{N}}\cdot e^{f(\{x\})}dx_{i}\ldots dx_{N} with respect to variance \epsilon. I find some difficulties...
  15. T

    Importance of homogenity of variance

    Hey all, When performing parametric statistical tests (especially t tests and ANOVA), why is the homogenity of variance important ? I mean why do these tests care if the samples have significantly different variance ? Is it because the methods used to determine the test statistics require...
  16. Matterwave

    Energy variance, and pair production

    Ok, so here's a question. The energy of say photons is frame-dependent. Photons are blue-shifted or red-shifted depending on my velocity towards or away from the source. However, what happens when I apply this to pair-production? For example, if my photons are energetic enough, they may create a...
  17. T

    Is the Square Root of an Unbiased Variance Estimator Also Unbiased?

    Hey all, In Schaum's outline it claims that the sample variance of s^2 is a biased estimate of the population variance because its mean is given by: \mu_{s^{2}} = \frac{N-1}{N}\sigma^{2} which I am cool with. It then says that the modified variance given by: \hat{s} =...
  18. D

    Expectation and Variance for Continous Uniform RV

    Homework Statement 8. Suppose that X and Y are independent continuous random variables, and each is uniformly distributed on the interval [0,1] (thus the pdfs for X and Y are zero outside of this interval and equal to one on [0,1]). (a) Find the mean and variance for X+Y. (b) Calculate...
  19. C

    What is the correlation of X and Z in terms of variance and covariance?

    Very sorry that I've double posted but I realized i placed the original post in Precalculus. 1. Homework Statement Question Let X and Y be independent random variables with variances 9 and 7 respectively and let Z = X - Y a) What is the value of Cov(X,Z) b) What is the value of...
  20. K

    Expectation and variance of a random number of random variables

    Homework Statement Let X1...XN be independent and identically distributed random variables, N is a non-negative integer valued random variable. Let Z = X1 + ... + XN (assume when N=0 Z=0). 1. Find E(Z) 2. Show var(Z) = var(N)E(X1)2 + E(N)var(X1) Homework Equations E(Z) = EX (E(X|Z))...
  21. D

    Statistical mechanics: energy variance of ensemble

    I posted this once already without seeing the rule that HW questions must go here--sorry :redface: So, the problem: I'm really lost on where to get started here. It's a two state system, one with energy 0 and the other with energy ε. I already have ensemble average, <E>, found to be: ε / (e^βε...
  22. D

    Statistical mechanics: energy variance of ensemble

    I'm really lost on where to get started here. It's a two state system, one with energy 0 and the other with energy ε. I already have ensemble average, <E>, found to be: ε / (e^βε + 1) , where β is thermodynamic beta, 1/KbT. How do I convert this to an expression for the variance of the...
  23. G

    Variance of bootstrap sample of size n

    http://img138.imageshack.us/img138/6060/98259799.jpg I have done part one and found that the bias is \frac{\theta}{n} then i don't know how to proceed. in my notes, have the following result, http://img189.imageshack.us/img189/9699/resultc.jpg i am thinking, this time i have to...
  24. G

    Estimating Population Variance from Observations

    Suppose the population variance \theta is to be estimated from observations Y_1, Y_2, \dots, Y_n using \hat{\theta} = \left(\frac 1 n \sum_{i=1}^n (Y_i - \overline Y)^2\right) where \bar{Y} is the mean. when it didnt say which distribution Y_is are? thanks
  25. S

    Variance of experimental data, compared to Theory

    I'm looking for a way to compare experimental and theoretical data and determining if it obeys a certain law. In particular, I'm writing a computer program that does this and at the moment what I'm doing is, I'm calculating the ratio of each reading with the theoretical result and calculating...
  26. S

    Can i get some help with an Analysis of variance table ANOVA?

    having a little trouble with the question below. its on a sample exam paper I'm doing. any help would be appreciated 155 hospital patients completed a questionnaire about their hospital stay. We examine the variables Satisfaction and Stay (length of stay). Stay is measured in days and...
  27. K

    Probability: Coinflips & Variance

    Homework Statement You are flipping a fair coin n times. Let X be the number of times you get a head followed by a tail (HT) and Y is the number of times you get tail and then a head (TH). Find Var(X) and Var(Y). Homework Equations Cov(X,X) = Var(X) The Attempt at a Solution My...
  28. D

    Variance of Sampling Distribution vs. Sample Variance

    Okie, I am confused. What is the difference between Variance of Sampling Distribution VS Sample Variance? Let me take a shot first... 1.) Sample Variance is just the variance of the sample, like u have 5 objects from a pool of 1000 objects... the sample variance is just the variance of the...
  29. G

    Understanding the Variance of a One-Dimensional Random Walk

    Hi, I know that the expectation E(Sn) for a one-dimensional simple random walk is zero. But what about the variance? I read in http://en.wikipedia.org/wiki/Random_walk#One-dimensional_random_walk" that the variance should be E(Sn2) = n. Why is that? Can anyone prove it? Thank you...
  30. P

    The average and variance of distributions (thermodynamics)

    (Note: I'm not sure about international notations or terms, but I hope everything is comprehensible) Next Monday I will pass my exam in theoretical physics about thermodynamics. However, there's still one thing that I couldn't find explicitly described in my lecture notes or any additional...
  31. S

    To calculate variance and CV from multiple (weighted) variables

    Hello everybody, My name is Sumet. I am studying in network traffic field. My background in statistic is not so strong; however, I have to calculate weighted sum of variables in order to determine variance and coefficient of variation (CV) of measured values. Please see the following...
  32. F

    Whats the formula for variance between batches?

    Im working on a lab for my Civil Engineering Materials class and its asking for the "between batch variation" (SBB^2) for different cylinders of Portland cement concrete. Its not written anywhere on the lab sheet. And I've looked in my book, notes, and Google. I am getting nothing here :/
  33. C

    Infinite Variance VS Zero Variance

    Hi there, this is caco, I´m a new user from planet Earth. I´m studying Information Theory and lately It seems that I live in a fractal ocean of gaussian distributions... I do know that zero variance processes relate to Dirac´s delta distribution, my favourite mathematical artifact ever...
  34. Y

    Question about what this variance value means

    i calculated the variance of a few measurements and i got the value of 3.65 i know the variance tells us the degree of dispersion from them ean value, and i came up with 3.65, what does this number say about the data?
  35. G

    Work out the variance of the gamma

    Hi, I'm trying to work out the variance of the gamma(I'm up the the part where you multiply x^2 by the function), but i don't know how to work out what \gamma(\alpha + 2) equals to i know I am supposed to use the fact that \gamma(\alpha + 1) = \alpha \gamma(\alpha) but i don't...
  36. F

    What Is the Variance of an Eigenvector in a Hermitian Operator?

    Homework Statement On page 5 of http://arcsecond.wordpress.com/2009/08/01/the-cauchy-schwarz-inequality-and-heisenbergs-uncertainty-principle/ the author states (w/o proof) that if \psi is an eigenvector (say with eigenvalue \lambda) of an Hermitian operator A (I don't think the Hermitian-ness...
  37. C

    Proving Inverse Gamma Variance: Step-by-Step Guide

    Hi! Can someone help me prove that the variance for the inverse gamma is: \frac{\beta^2}{(\alpha - 1)^2 (\alpha -2)} I started with: E(x) = \int_0^\infty x \frac{\beta^{\alpha}}{\gamma(\alpha)}(\frac{1}{x})^{\alpha + 1} exp (\frac{-\beta}{x}) dx then i let y = \frac{\beta}{x}; dy =...
  38. A

    Variance of the union of two samples

    This seems like a simple problem but I cannot find an answer. Imagine I have 2 bags of samples with estimated means \hat{x} and \hat{y} and estimated variances \hat{\sigma_x} and \hat{\sigma_y}. The bags contain n and m samples respectivelly. Now assume I mix all the samples in a single...
  39. M

    Simple sample variance problem

    The length of time, in minutes, for an airplane to obtain clearance for takeoff is a random variable Y = 4X + 2, where X has the density function: f(x) = 1/3 e^(-x/3) for x > 0 Find the variance of Y. ----- I found the expected value of X to be 14 minutes, which was correct. This...
  40. M

    Expected value of sample variance

    Hi, My question is related to this web page. http://en.wikipedia.org/wiki/Estimator_bias In the Examples section, note the equation for the expected value of sample variance. {E}(S^2)=\frac{n-1}{n} \sigma^2 Could anybody please show me the steps to go from the sample variance...
  41. R

    Can Coefficient of Variation Determine the Best TV Manufacturer?

    coefficient of variance ? ok i know that coefficient of variance is calculated using the equation CV=(standard deviation /mean value)*100... here is my problem ..Two TV manufacturing companies have provided the mean values and SD of the life time of their TVs .after calculating for one...
  42. S

    What is the difference between auto-correlation and cross-correlation?

    What is the difference between Auto-correlation and auto-variance? The same for cross-correlation and cross-variance?
  43. S

    Variance Problem: Calculating P(X1 > 90), E(Y), Var(Y) & P(Y>16*90)

    X1, X2,...,X16 are independent and normally distributed, where mean value is 80 and variance is 18^2. Let Y = X1 + X2 + ... + X16. Calculate i) P(X1 > 90) ii) E(Y) iii) Var(Y) iv) P(Y>16*90) i) 0.288, easy ii) E(Y) = 16*80 = 1280 iii) Var(Y) = Var(16*Var(X)) = 16^2 * 18^2...
  44. S

    Why Do CO2 Levels Vary During Glacial and Interglacial Periods?

    There is an unexplained mystery as to why atmosphere CO2 levels varies long term (geologically) and short term (glacial/interglacial cycle.) Contrary to what is repeated in many blogs the glacial/interglacial cycle changes of about 90ppm to 100 ppm is not due to colder oceans being able to hold...
  45. J

    Multiplying random value by variance + motivation

    Just a quick question. If you want any value to follow a particular probability distribution function (pdf), do you have to multiply that value by the variance of the desired pdf ?
  46. F

    Help with proof of sample variance

    Hi, I'm trying to prove to myself that the formulation of sample variance as s^2=\frac{1}{n-1}\sum_{i=1}^{n}(y_i - \mu_y)^2 is an unbiased estimator of the population variance \sigma^2. Of course, I proceed by checking the expected value of the sample variance, which flows smoothly until I...
  47. Cyrus

    Why Divide by n-2 in Least-Squares Error Variance Calculation?

    In the textbook it says this: http://img6.imageshack.us/img6/1896/imgcxv.jpg Where does this hocus pokus 'it turns out that dividing by n-2 rather than n appropriately compensates for this' come from?
  48. V

    Calculating Mean and Variance for Graduation Ceremony Guest Tickets

    Homework Statement Suppose that, on average, 70% of graduating students want 2 guest tickets for a graduation ceremony, 20% want 1 guest ticket and the remaining10% don't want any guest tickets. (a) Let X be the number of tickets required by a randomly chosen student. Find the mean and...
  49. T

    Variance of a harmonic motion particle

    Homework Statement Consider a particle in the harmonic potential V(x)= \frac{m\omega^2 x^2}{2} . Its lowest energy eigenvalue is E_0=\hbar \omega/2 and the eigenfunction associated with this energy, ie the ground-state wave function, is \phi_0(x) = \left(\frac{m\omega}{\pi...
  50. H

    How Do You Compute Var(X-2Y) When X and Y Are Not Independent?

    Studying for an intro course test and I have no one to compare it to right now.. any help would be appreciated. Here is the question. Q. Suppose X and Y are random variables such that p(X,Y)=1/3, Var(X) = 9 and Var(Y) = 1. Compute Var(X-2Y). Since X and Y are not independent, we are...
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