Variance Definition and 357 Threads

So in computing the variance-covariance matrix for β-hat in an OLS model, we arrive at VarCov(β-hat)=(σ_ε)^2E{[X'X]^-1} However, I'm incredulous as to how X is considered non-stochastic and how we can just eliminate the expectation sign and have VarCov(β-hat)=(σ_ε)^2[X'X]^-1 I'm...

So for example, if I have a random variable X, take it to be normally distributed. How do you find the expectation and variance of the random variable e^X in terms of μ and σ? Integrating the entire normal function with the f(x) is it?

Does the speed of light vary with different frequencies(or wavelengths) in mediums other than vacuum, or is it constant for all light regardless the frequency?

I'm studying on statistics. Then, I saw 'Kurtosis', that represents 'peakness' of the distribution. In the text, the kurtosis is defined as 4-th central moment devided by square of variance. But, I can't understand why the standized 4-th central moment is used. What is the role of the...

Hello all This is not homework, i work in engineering. I have some data in a table, there are 3 columns and 5 rows. The data relates to how high or low one rail is to the other. The data was collected across 3 days. At each 7m intervals the height of the right hand rail was...

Homework Statement I need to know these formulas to answer the homework problems, but I can't squeeze the forumlas out of the gibberish in the book, so I'm asking for varification of the formulas. For a bivariate probablity density function, for example f(x,y)= 2xy when x and y are...

I've made a 2D walker to compare different RNG's. I'm measuring the succes of each walk as the distance from the origin to the endpoint, using the regular 2-norm. The thing I can't seem to work out is the variance. D_n=\sqrt(x_n^2+y_n^2) Var(D_n)=E[D_n^2]=E[Z_1^2+...+Z_n^2] Since...

Homework Statement Let G be a random graph on n vertices: 1) What is the expected number of triangles in G? 2) What is the variance in the number of triangles? Homework Equations N/A The Attempt at a Solution I think I can do (1) by using indicator variables. In particular, let...

Homework Statement Suppose that a married couple in Canada decide to have babies until they get the first girl baby. It is well-known that in high-latitude countries, the chance of have a girl is slightly higher than the chance of having boy. Suppose that the chance of having a girl in Canada...

Homework Statement Suppose X1 , X2 , . . . , Xn are independent random variables, with common expectation μ and variance σ^2 . Let Sn = X1 + X2 + · · · + Xn . Find the variance of Sn. The attempt at a solution Expected value: E[S_n] = n E[X_i] = n\mu \hspace{10 cm} (1)...

Homework Statement Given that the natural log of the growth consumption rate is conditionally normally distributed. I am trying to convert it to a lognormal distribution, but I keep getting a variance that is different from what is in the solution manual. The problem is #3 in the document below...

Give an example of a random variable (i.e. give the range of values it takes and its p.m.f.) with the following properties: EX = 4, VAR(X)=4. Now give an example of a random variable with a different p.m.f. than...

need urgent help with a conditional variance proof. I have been given this problem and I'm pretty stumped. I want to prove that Y=g(X) if and only if var(YlX) = 0. so if var(YlX)=0 then E(Y^2lX) - E(YlX)^2 = 0 E(Y^2lX) =E(YlX)^2 so what should I do now? I tried showing that this...

This should be rather simple bayesian problem, but I can't figure it out for myself. If i pick numbers from normal distributionS, where the variance of the distribution at each pick v1, is in turn picked out of a normal distribution with variance v2. What is then the distribution of the...

[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...

Hi, Can a few of you please review the approach I plan to take for obvious errors? I have 50 subjects and each have a measure taken on the same variable before and after treatment. So, this is standard paired t-test time, but what I am actually interested in is the variance of the treatment...

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...

Homework Statement Assume a one way variance analysis model on the form: Y_{ij} = \mu + \alpha_{i} + e_{ij} where e_{ij} independent with expectation 0 and constant variance z_{ijl} = \left\{ \begin{array}{rcl} 1 & \mbox{for} & 1 \\ 0 & \mbox{else} \end{array}\right show that: a)...

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...