Variance Definition and 329 Threads

[solved]Expected Value and Variance Hi, I have a problem on Expected Value and Variance, and having spent hours but still couldn't figure out :( One state lottery has 200 prizes of $1 100 prizes of $5 40 prizes of $25...

Hi If I have measured the resonance frequency of three sets of resonators and calculated the mean, variance and standard deviation for each set. How do I add the three variances and standard deviations to get an overall variance and standard deviation? Well, I know that the standard...

In the Nuclear Magnetic Resonance, do the applied magnetic and electromagnetic fields correspond linearly to the heat generated? If not, how do they vary? Gracias

Well, just as I thought I'd got the hang of this... Koosis: Statistics: A Self-Teaching Guide, 4th ed., §§ 6.29-43. The "degreeses of freedom" are 3 and 36. This critical value, 4.38, is found by looking up the score for 1% in the table at the back of the book, or in Excel with...

I have a list of chemicals, their assay test results, and a binomial column of whether or not the assay test result was high enough to be considered a threat (anything >2g/ml). Some chemicals were tested more than once, but others were not. It is understood that it is a poor set of data, but I...

I'm reading a stat textbook and it says the following: Let a discrete-time random walk be defined by Xt = Xt-1 + et, where the et's are i.i.d. normal(0,σ2). Then for t≧1, (i) E(Xt) = 0 (ii) Var(Xt) = t σ2 However, the textbook doesn't have a lot of justifications for these results and...

I'm bad at stochastics so really glad for any help Homework Statement I have two normally distributed NON INDEPENDENT stochastic variables X~N(muX,sigX^2) and Y~N(muY,sigY^2) A third variable D is defined as D = sqrt(X^2 + Y^2). Since Y and X are stochastic D will also be stochastic...

Homework Statement show whether the system y(t) = x(2t) is time variant or notHomework Equations a system is time invariant if a time shift in the input signals results in an identical time shift in the output signal, that is if y[n] is the output of a discrete-time, time invariant system...

Homework Statement A function g is \alpha-regularly varying around zero if for all \lambda > 0, \lim_{x\to 0} \frac{g(\lambda x)}{g(x)}=\lambda^{\alpha} For real s and \alpha \in (0,1), define f: f(s)=1-\alpha \int_{0}^{\infty} e^{\alpha t}...

Homework Statement Lets say I roll 2 fair dice and take the sum of the square of each dice. What formula will be the variance? Homework Equations var(x)=e(x^2)-e(x)^2The Attempt at a Solution For dice A; E(A)=3.5 E(A^2)=91/6 ^ same for dice B. VAR(A^2+B^2)=E(A^4)-E(A^2)^2+E(B^4)-E(B^2)^2 ?

I am new in statistic. I come across the sample variance calculation in a book and it explains that denominator is divided by n-1 instead of n is because variance in samples will be likely to be lower than the population variance, so we divide by n-1 to make the variance larger. However, when...

Homework Statement Let Y denote the number of heads obtained when three fair coins are tossed.The variance of Y2 is Homework Equations The Attempt at a Solution MY problem is understanding what Y2 is. i have tried to calculate VAR(Y*Y) but my answer is wrong

Homework Statement Show that for identically distributed, but not necessarily independent random variables with positive pairwise correlation ρ, the variance of their average is ρσ^2 + (1-ρ)σ^2/B. ρ - pairwise corellation σ^2 - variance of each variable B - number of samples...

Hi all, I know about these facts: 1- The variance of importance weights increases in SIR (also know as the degeneracy problem). 2- It's bad (lol), because in practice, there will be a particle with high normalized weight and many particles with insignificant (normalized) weights. But I...

Hi, I am trying to estimate variance for negative Binomial distribution using maximum likelihood estimation and Expected (Fisher's) information to determine its variance. I know what variance is for this distrubution but I cannot derive it. Here is my solution. Any comments and...

I'm wondering if the sample mean \sum{x_i}/n and sample variance \frac{1}{n-1}\sum{(x_i-\bar{x})^2} is always an unbiased estimate of the true expected value and variance of the random variable X, where x_i are iid samples. Or at least asymptotically unbiased. I don't think it is, since the...

is known that the Tomato crop (in ton) in some farm are Sampled for 10 years. the Standard deviation of the crop was 2 ton. the Income (Y) from the Tomato Depends on the crop (X) according to following connection Y=3X-2 the Variance Income from the Tomato in this Sampled is 4? if i...

Does anyone know the formula for an unbiased estimator of the population variance \frac{1}{n}\sum_{i=1}^{n}(x_i - \bar{x})^2 when taking r samples without replacement from a finite population \{x_1, \dots, x_n\} whose mean is \bar{x}? A google search doesn't find anything useful other than the...

Say we have a sample of test scores, all marked between 0 and 100. Does the sample variance have to be less than or equal to the maximum mark 100 or can it exceed this?

It is defined that the population variance is S^{2}= \frac{1}{N-1}\sum^{N}_{1}\left(y_{i} - \bar{y}_{N}\right)^{2} or \sigma^{2}= \frac{1}{N}\sum^{N}_{1}\left(y_{i} - \bar{y}_{N}\right)^{2}. Also that the V\left[\bar{y}_{n}\right] = \frac{N-n}{N}\frac{S^{2}}{n} = \left(\frac{1}{n} -...

Homework Statement It is given a function y(t)=ae(t) where e(t) is the "[URL error function [/URL] I am looking for the variance of this function in an infinite space. Since t is time, I assume that this space is defined as [0,+∞). Thus, the usual variance functions does not apply since...

Homework Statement A sample of size n is drawn from a population having N units by simple random sampling without replacement. A sub-sample of size n_{1} units is drawn from the n units by simple random sampling without replacement. Let \bar{y_{1}} denote the mean based on n_{1} units and...

The attached equation is from http://en.wikipedia.org/wiki/Multivariate_normal_distribution can anyone show me why the conditional variance is equal to (1-rou^2)* variance of y thanks

Hi, I want to proof what the distribution will be when I apply a normal distributed x to a linear function y = a*x + b. What will be the mean and the variance of y ? The expectations can be calculated than with this formula ( probably with this formula what i want can be proofed with...

Homework Statement N=a^+a a=\frac{ip+mwx}{\sqrt{2m\hbar w}} \quad a^+=\frac{-ip+mwx}{\sqrt{2m\hbar w}} |z>=e^{\frac{-|z|^2}{2}}\sum^{\infty}_{n=0}\frac{z^n}{\sqrt{n!}}|n> where <n|n>=1 Show that the variance (uncertainty) in N, \Delta N is |z| i.e. calculate (\Delta...

Homework Statement Why is it normality is much more important for making a confidence interval for the mean than for the variance? You do use the estimated variance to make the mean confidence interval. So why is the mean confidence interval more robust against the normality assumtion...

Let Y by the number of heads obtained if a coin is tossed three times. Find the mean and variance of Y^2. For the mean I get, (0+1+4+9)/4=7/2, and for variance I get (0+1+16+81)/4 - (7/2)^2 = 49/4. Is this correct? For the following question, I'm not sure how to begin: Show that if T...

I want to calculate expected variance of a randomly selected subset of a population. The particular problem I am trying to solve is as follows. There is a set of values X = {x1, ... , xn}. Let Y be subset of X with n-1 elements. I think that if Y is selected at random (that is, if is...

Hello, we are given N independent random variables z_i defined as follows: z_i = \theta + v_i where the r.v. v_i are zero-mean normal distributions v_i \sim N(0,\sigma^2). I want to compute the variance of the estimator \hat{\theta}=\frac{1}{n}\sum_{i=1}^n z_i However I can't...

1. A necklace consists of 5 beads on a string. The beads for making the necklace are drawn at random from a box containing a very large number of beads. 2/3 of the beads are pink and 1/3 are blue. find the mean and variance of the number of unlike pairs of adjacent beads in the necklace. I am...

In the Searle's 1971 book Linear Model, page 57, has a formula for the Variance of Quadratic form: var(Y^{T}AY)=2tr(A\SigmaA\Sigma)+4\mu^{T}A\SigmaA\mu The proof of this showed on page 55 was based on MGF. I'm looking for proofs are less complicated. Some thing that is similar to show the...

Suppose that Y is a random variable with moment-generating function m(t) and W = aY + b, with a moment-generating function of m(at) * e^(tb). Prove that V(W) = V(Y) * a^2. I have done an absurd amount of work on this problem, and I know its actual solution doesn't have one and a half pages worth...

Homework Statement How do I calculate the variance of \frac{1}{\log{X} + 2} where X is a random variable? The Attempt at a Solution Is it: \frac{1}{\log{var(X)}} Homework Equations The Attempt at a Solution

A computer can generate random numbers which are either 0 or 2. On a particular occasion, it generates a set of numbers which consists of 23 zeros and 17 twos. Find the mean and variance of this set of 40 numbers. Please help i just don't know where to start. In fact i am thinking of...

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...

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 =...

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...

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) =...

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...

How to prove the variance of the t distribution?

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) ?

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

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...

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...

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...

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...

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...

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...

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} =...

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...