Variance Definition and 329 Threads

If I have a set of indepenent and identically distributed random variables X1,...Xn, then Var(\sum_{i=1}^{n}X_i) = \sum_{i=1}^{n}Var(X_i). Now I want to know what the sum of variances of Xi would be when n is a random variable? I'm guessing the above statement still holds when n is a random...

[SOLVED] Properties of variance Would the Var(aX + bY + c) just be the Var(aX+bY) since adding a single number to the function doesn't change the variance. I would then be able to use the property: Var(aX+bY)= a^2Var(X)+b^2Var(Y)+2abCov(X,Y) Just wondering if anyone can confirm my...

Given |Psi> = a|up>+b|down>, in principle it should not be so difficult but when I calculate Delta S=Sqrt[<S^2_x,S^2_y, or S^2_z>-<S_x,S_y, or S_z>^2] the second term gives the problem. Lots of many terms a*, a, b*, b which is not canceled involve. Whoever knows the way to get rid of...

Hi All: If given a set of 3D points data, it's very easy to calculate the covariance matrix and get the principle axises. And the eigenvalue will be the variance on the principle axis. I have a problem that if given a random direction, how do I calculate the variance of the data on the given...

[SOLVED] Help with variance sum + correlation coefficient formula This is a worked example The objective is to prove -1 \leq \rho(X,Y) \leq 1 Then the book uses this formula... (2) 0 \leq Var(\left \frac{X}{\sigma_x} + \frac{Y}{\sigma_y} \right) (3) = \frac{Var(X)}{{\sigma_x}^2} +...

Homework Statement Compute the variance of the random variable X given by V(X) = \sqrt{E((X-E(X))^2)} where E(X) is the expectation value of random variable X Homework Equations Hint: Use parameter differentiation The Attempt at a Solution I have no idea what to do here. I've never taken...

As it often said, the majority of the variation in the human genome is due to intra-group variation, not inter-group variation (I think .85 is the number due to intra-group variation). I know what this intuitively means, but can anyone explain to me what it rigorously means? (in statistical terms?)

Can anybody explain to me how to get the mean and the Variance for a specific function. Thanks alot.

the Cosmic Variance blog has changed format and eliminated a nice feature that used to keep discussion threads alive. on the righthand margin of front page, it used to list which posts had recent comments and, in small font, WHO THE COMMENTERS WERE so if some interesting people, such as Lee...

I'm trying to see how well my data fit a certain probability distribution (an exponential distribution) and I basically want to know how reliable is it to compare the the theoretical variance of the distribution and the variance of the data, to assess the goodness of fit of data to a...

Sad disconnect at Cosmic Variance blog---how not to discuss Cosmic Variance blog is known for lively discussion but I just noticed a sad disconnect where the key point Lee Smolin was making just slipped by in a "yes it is---no it isn't" kind of way without any reasoned counterargument. It is...

Hi all: If I have a dataset V of the size n*1. Assume that the mean of the dataset is 0 and var(V)=x is its variance. If I want to modify this dataset so that the variance of the new dataset will be var(V_hat)=y. The errors are spreaded average on each element in the dataset. What I did is...

1. 'Find an expression in terms of x for the variance of: 9,4,x,3' Give your answer in the form of ax^2 + bx + c I would usually give you some information of how I could possibly tackle this question but unfortunately I have no idea. Could someone shed some light? Thanks

if a random variable X has variance sigma, does it mean that the average variance of X will be sigma, or will X always have variance sigma. So if I did 10 simulations of the random variable X, is it plausiable that the variances differ widely, but the average of the variances converge to the...

How do I approach finding variance of sample mean of Poisson distribution? thanks.

I'm having a problem with my answer for a question involving finding the mean and variance of a function. I'll state the question and list the steps I did so maybe you guys can see where I went wrong. The question is: Given Y = |tan(X)| and X is uniformly distributed on (-pi/2, pi/2) Find a)...

Hopefully someone will be able to help me. I am trying to derive the formula for variance of variance for a sample. This would be similar to variance of a sample mean which is sigma/sqrt(N). I know the variance of sample variance is sigma^2 * sqrt (2) / N, but I can't prove it...

an urn contains 4 red balls and 4 white balls an experiment consists of selecting at random a sample of 4 balls and recording the number of red balls in the sample setup the probability distribution and compute its mean and variance i know what a probablity distribution is. can someone please...

Hey all, I am currently working on the statistics part of my Master thesis and I am conducting an ANOVA test to compare mean variances between three samples. Four out of the 15 compared variables do not satisfy Levene's test for equality of variance.:cry: I know that ANOVA is relatively...

I think it is easy but I can't figure it out. :( any help?

Does anyone know how to calculate the variance of the variance estimator of normal distribution? x_i, i\in\{1,2,...,n\} are n samples of normal distribtuion N(\mu, \sigma^2). And S^2 = \frac{n}{n-1} \sum_i (x_i - \bar x)^2 is the variance estimator, where \bar x = \frac{1}{n} \sum_i x_i...

the discrete prob distribution X/Y - G - D 0 - 0,1 - 0,15 1 - 0,1 - 0,3 2 - 0,05 - 0,3 this is what i have so far: E[X|Y=D]=0,2 E[X|Y=g]=0,9 E[X]=0,725 E[X^2|Y=D]=0,3 E[X^2|Y=G]=1,5 Var(X|Y=G)=0,69 Var(X|Y=D)=0,26 i.e. [X]=0,2*0,25 + 0,9*0,75=0,725 is the previous...

Having a lot of trouble with a particular problem in the topic of variance. The problem is: "Suppose you are organizing a game where you charge players $2 to roll two dice and then you pay them the difference in scores. What is the variance in your profit from each game? If you are playing a...

I have trouble understanding operators and observables: Does <A> the average value of an observable and the variance depend on the state of the system? What does it have to do with the Hamiltonian? Thanks!

Suppose you are conducting a hypothesis test to compare two sample means from independent samples, with the variance unknown, but you know it is the same for both populations. Then you use the pooled estimate of the variance given by [ (n1 - 1)s1^2 + (n2-1)s2^2 ] / (n1+n2-2) I was just...

I have just started University and we have been doing t-tests however in our Computer labs we are supposed to do the Levenes Test. I have done the levenes test from our data of males and female heights in our class. i was just wondering what a value of F = 0.001 and Sig. 0.982 would mean. the...

So i need to find the variance of a number of dice rolls. I know that i use the following formula: N ∑ ( X i - µ)2 i = 1 σ2 = --------------- N but i don't know how to use it. I feel really stupid asking this but i am really lost right...

*** PART I. *** THREE QUESTIONS ON "COULOMB'S LAW" The value of the constant "K" in what appears to be the "ORIGINAL" Coulomb's Law depends upon the nature of the medium. [ K = 1/4pi*epsilon ] where epsilon is the "absolute permittivity of the medium". In many modern books, I...

I am having trouble with this question. Let X equal the number of flips of a fair coin that are required to observe the same face on consecutive flips. (a) Find the p.m.f. of X. if found the p.m.f. to be f(x) = (\frac{1}{2})^{x-1} for x=2,3,4,... (b) Give the values of the mean, variance...