Variance Definition and 329 Threads

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...

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))...

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...

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...

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...

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

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...

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...

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...

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...

(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...

Im working on a lab for my Civil Engineering Materials class and its asking for the "between batch variation" (S[SIZE="1"]BB^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...

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...

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?

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...

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...

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 =...

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...

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...

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...

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...

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

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...

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...

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 ?

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...

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?

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...

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...

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...

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...

Hi everyone, Anyone out here who knows how to use MATLAB to generate rate random walk, angle random walk and flicker noise and to c wat is the allan variance plot like. Need the code to implement allan variance plot in particular. Thank you

I am looking for methods to calculate the error in a slope. the caveat is that my values themselves are averages with a STDEV. E.g. x 1+-1% 2+-1% 3+-1% y 0.14+-0.01 0.27+-0.02 0.42+-0.02 (using...

Calculating the variance with a TWIST! Hello! I am trying to understand this problem! its just on my practice questions and Ihave the answer, I CAN NOT understand how to set it up! PLEASE someon ehelpo! THis is it :) A student wants to calculate the variance of a set of 10 scores. But he...

Homework Statement X1 and X2 are independent random variables. They both have the same mean (mue). Their variances are s1^2 and s2^2 respectively, where s1^2 and s2^2 are known constants. It is proposed to estimate mue by an estimator T of the form T=c1X1 + c2X2. Show that T will be...

I think I'll ask it this way. Here goes... 1 point = zero dimensions. 2 points = 1, which is line; 3 points, shape; 4 minimum to have volume. Somewhere, or rather, when, time applies, most preferably at that case in which dimensionality, quite plainly, is. My question follows a...

Homework Statement If there are 4 children in a family, find the probability of getting exactly 3 girls. Find the mean, variance, and standard deviation. Use two different methods(binomial distribution method and general probability distribution method). Homework Equations Binomial...

Hi, my girlfriend is taking a business statistics class and she had a test today. she got stumped on a question and wrote it down so she could ask me about it when she got back since I'm pretty good at math. I tried solving it but from what i can tell it seems like you would need to know the...

Hi, my girlfriend is taking a business statistics class and she had a test today. she got stumped on a question and wrote it down so she could ask me about it when she got back since I'm pretty good at math. I tried solving it but from what i can tell it seems like you would need to know...

I know Var(aX + bY)... I know Var(XY)... I don't know of a solution to Var(X/Y)... is there one?

Homework Statement The data below: I(A): 6 12 18 24 F(R): 240 120 80 60 Rearrange the values of R so that a straight line graph will result. Homework Equations I have to find a proportional equation for I and F. Something like I = F The Attempt at...

ok guys , i need an answer to this question , use both moment generating function and cummulative function to show that z=(x(bar)-\mu)/(\sigma/\sqrt{n}) if x(bar) is based on a random sample of size n from a normal(\mu,\sigma^2)

To All, I did a study and my response is defined as y = b1x1 + b2x2 + e where e ~N(0,1). I have y~N(4,33). In my data results, I did an ordinary least squares regression model for y = b1x1+b2x2+ e. The ANOVA is telling me the mean of y is 4, but MSE is 1. So here is my question. If I...

Ok I know that Var[X] = E[(X-E[X])^2]. But I just can't help but think that the variance should always be zero. I think it makes so much sense, but obviously the formula says otherwise... But look, my reasoning seems so perfect: 1) The variance is the expected difference from the mean...

The value of a real-world resistor ( ) changes with significant time as the resistor conducts a current. Answer choices Never Rarely Sometimes Usually Always Explain why.

find the variance for f(x)= 1/4 for -2<x<2 & 0 elsewhere The first thing I did was find the expected value, which was 1 (just integrated the original function from -2 to 2). Then I set up the next part as \int (x-1)^2 (1/4) dx with the limits -2 to 2 So it became 1/4\int x^2-2x+1 dx...

If I have a sample consisting of n measurements why is the sample variance the result of dividing by n-1 instead of n? jf

Homework Statement The sample mean and sample variance of five data values are, respectively, 104 and 4. If three of the data values are 102 100 and 105, what are the other two values?The attempt at a solution My idea was to get two equations for the two unknowns, let's call them x and y. The...

Homework Statement I am given the table \begin{array}{ccccc} samplesite & 1950 & 1975 & Change \\ 1 & 7.30 & 7.70 & 0.40\\ 2 & 6.14 & 6.72 & 0.58 \\ 3 & 6.47 & 6.32 & -0.15 \\4 & 5.87 & 6.38 & 0.51 \\ 5 & 6.06 & 6.34 & 0.28 \\ 6 & 4.71 & 5.78 & 1.07 \\ 7 & 5.45 & 5.59 & 0.14 \\ 8 & 6.17 &...

Let X, Y be independent exponential random variables with means 1 and 2 respectively. Let Z = 1, if X < Y Z = 0, otherwise Find E(X|Z) and V(X|Z). We should first find E(X|Z=z) E(X|Z=z) = integral (from 0 to inf) of xf(x|z). However, how do we find f(x|z) ?