Variance Definition and 329 Threads

I attached a pdf. The questions are not really what is stumping me. Its the wording of the question I don't understand. When it says, "Assume that 0 < λ < 1. Note that your answers will be in terms of the constant λ." and "Assume that λ > 0. Note that your answers will be in terms of the...

A robot arm solders a component on a motherboard. The arm has small tiny errors when locating the correct place on the board. This exercise tries to determine the magnitude of the error so that we know the physical limitations for the size of the component connections. Let us say that the...

I have the continuous random variable Y, defined such that: Y=3X+2 and the PDF of x is zero everywhere but: f(x)=\frac{1}{4}e^{\frac{-x}{4}}, x>0 I correctly got the mean like so: \mu=E(h(x))=\int^{\infty}_{0} h(x)f(x) and evaluated it to be 10. I am unsure as to how I go about...

Hello, I consider myself an up-and-comer theoretical physicist (although getting a bit of a late start), and there's something that continues to trouble me about the way physics is taught both professionally and popularly, and I want to survey how others feel about the issue. The issue is the...

Homework Statement Calculate variance of 34.1, 35.6, 35.8, 34.3, 32.9, 33.7 Homework Equations The Attempt at a Solution A set of numbers: 34.1, 35.6, 35.8, 34.3, 32.9, 33.7 I have calculated the variance to be = 0.208 Would it be better to quote to three sig fig as I...

Let's assume there's a magical ball that bounces once every .5 seconds, and that there was a specific machine designed to calculate the rate of the ball's bounce (with error). After performing numerous readings of the ball's bounce using this machine, you have a collection of values describing...

Homework Statement I am trying to follow a step in the textbook but I don't understand. var\left(\frac{1}{N}\sum_{n=0}^{N-1}w[n]\right)\\ =\frac{1}{N^2}\sum_{n=0}^{N-1}var(w[n]) where w[n] is a Gaussian random variable with mean = 0 and variance = 1 Homework Equations Var(X) =...

Homework Statement The problem wants me to calculate (Δx)^2 and (Δp)^2 to find the uncertainty principle. Delta x is the variance and the problem gives the formula as.. Δx= <n|x^{2}|n>-<n|x|n>^{2}Homework Equations x=\sqrt{\frac{\hbar}{2m \omega}}(A^{-}+A^{+}) Where A+ and A- are the raising...

I'm reading a finance book in which the author proposes to exclude the mean when calculating the variance of returns, because he thinks it's difficult to distinguish the drift of the price from the variance of that time series. So he basically calculates the sample variance like this...

Hi, I was looking at the way variance is calcullated. Let us say V represents variance, then V = average of the sum of squares of the difference between Xi and the mean (μ) What I do not understand is why square the difference? By squaring are we not magnifying the difference by many...

Homework Statement Assume that X is squared-Chi-distributed, which means that the moment generating function is given by: m(t)=(1-2t)^{-k/2} Use the mgf to find E(X) and var(X) The Attempt at a Solution I know that m'(0)=E(X), and m''(0)=var(X). So I find...

So l have a nuclear counting system which follows a poisson distribution. I have taken 5 data sets consisting of 30 counts each and l have used them in a chi squared gof test to see if they follow a poisson distribution. For each data set my p-value has been changing. Initially it was 0.5 then...

Could some help with a question? Any hints or directions on how to approach would be greatly appreciate it. The question: http://s12.postimage.org/kvtyiacuj/question.png Thanks!

Let Pr(X_{i} = +1) =\frac{2}{3} = 1 - Pr(X_{i} = -1) , and S_{n} = \sum{X_{i}}, For each k≥1, define T_{k}\ =\ min \left\{n≥1: S_{n} = k \right\}. Calculate E[T_k], and Var[T_k]. 2. Homework Equations E[T_k] = \sum_{n=1}^{n=∞}{n Pr(T_k = n)} , and E[T_k]^2 = \sum_{n=1}^{n=∞}{n^2 Pr(T_k...

Homework Statement Let \bar{X}1 and \bar{X}2 be the means of two independent samples of sizes n and 2n from an infinite population that has mean μ and variance σ^2 > 0. For what value of w is w\bar{X}1 + (1 - w)\bar{X}2 the minimum variance unbiased estimator of μ? (a) 0 (b) 1/3 (c) 1/2 (d) 2/3...

Homework Statement For n trials, S_n can be seen as the sum of n independent single trials X_i, i = 1,2,...,n, with \mathbb{E}[X_i]=p and Var[X_i]=p(1-p).2. What I don't understand I don't understand why Var[X_i]=p(1-p). We know that: Var[X_i]=\mathbb{E}[(X_i - \mathbb{E}[X_i])^2] =...

Suppose we have a normal distribution and a sample of n values from the normal distribution. To estimate the variance we can use the standard sample variance formula ( average squared distance from the mean divided by either n ( biased estimator ) or n-1 ( unbiased estimator ) ). There is...

I already have the full solution to this so I'm not looking for an answer, I am hoping to get an explanation of certain parts that are unclear. Question: A random variable X has the following CDF: f(x) =\left\{ \begin{array}{lr} 0& x<0\\ \frac{x^2-2x+2}{2} & 1 \le x < 2 \\ 1 & x \ge 2...

I am working on studying for a probability exam and I just came across conditional variance, but I can't find anything in my materials for how to solve it. If I want to find the conditional variance of Y given that X=x, or Var[Y|X=x], how would I solve it? I am given a continuous distribution...

I am working on studying for a probability exam and I just came across conditional variance, but I can't find anything in my materials for how to solve it. If I want to find the conditional variance of Y given that X=x, or Var[Y|X=x], how would I solve it? I am given a continuous distribution...

Hi All, Is it possible to express the kurtosis \kappa, or the 4th central moment \mu_4, of a random variable X in terms of its mean \mu = E(X) and variance \sigma^2 = Var(X) only, without having to particularize to any distribution? I mean, an expression like \kappa = f(\mu, \sigma^2) or \mu_4...

Hi, I have a pretty simple question which I thought I do not need to make a topic about, but Google is actually not helping, which is surprising. So here it goes: How can white noise have infinite power if its variance is finite? As far as I am aware, the following is always valid for a...

Hello Everyone! What $b$ minimizes $E[(X-b)^2]$ where $b$ is some constant, isn't it $b=E[X]$? Is it right to go about the proof as follows: $E[(X-b)^2] = E[(X^2+b^2-2bX)] = E[X^2] + E[b^2]-2bE[X]$, but $E[b] = b$, we differentiate with respect to $b$ and set to zero, we obtain that $b=E[X]$...

Sorry it's my first time posting so I am not sure if latex works here... I have been trying to understand the proof of WLLN using Chebychev's inequalities, and here are my problems: I know for the Strong Law of Large Numbers, if n→∞, Ʃ(1 to n) σi ^2 / i^2 < ∞ => SLLN is satisfied...

Hi I've got an ARMA model, and I am struggling to theoretically quantify the benefit of using it to generate forecasts for various lead times, compared to using the mean level of the process. I think the ratio of variance of forecast error using ARMA to variance of forecast error using the mean...

Homework Statement I want to calculate the variance of a linear combination (b1, b2, b3, b4, b5, b6). I know what the variance equation is but I'm not sure if I have expanded it right. Homework Equations http://en.wikipedia.org/wiki/Variance The Attempt at a Solution Var(b1, b2, b3, b4...

Homework Statement Homework Equations The Attempt at a Solution I'm confused actually how to go about this. Sounds very simple, but when i do what they suggest, 'first, find the variance of (n-1)s2/σ2 i get larger variances rather than smaller, which makes no sense. should...

The variance equation basically sums up all the distances between each data value and the mean of the set. The interesting thing is that each distance and squared for a reason that I believe is to make the distance positive, but why don't the statisticians just take the absolute value of each...

Homework Statement Homework Equations The Attempt at a Solution Was able to get the population mean of 5.3 with 4*.2 + 5*.4 + 6*.3 + 7*.1 But for some reason I'm drawing blank for the variance (which i guess is .81)

Homework Statement let x_{i} be a random variable, and let y_{j} = \sum x_{i}. The variance of the random distribution of the x_{i}'s is known, and each y is the sum of an equal amount of x_{i}'s, say N of them. How do I compute the variance of y in terms of \sigma^2_{x} and N? Homework...

Homework Statement Find the Mean and Variance of Random Variable Z = (5x+3) Using data set:Using: & The Attempt at a Solution

Hi. i wonder how come one doesn't divide with (n-1) when finding the sample mean variance. Homework Equations Shouldn't I divide with n -1 since it is samples i am dealing with? The Attempt at a Solution I don't really have any idea as to why the book uses n. I have googled but...

http://bildr.no/view/1115383 i wonder if anyone could explain the proof for theorem 4.3 i have understood definition 4.3

Hello there, I am wondering if somebody could help in an issue far from my expertise. I have some data which is reasonable to conjecture could be modeled with a random walk with drift. I am struggling though to understand how to estimate from the empriic data the most likely drift and...

I am trying to match little square patches in an image. You can imagine that these patches have been "vectorized" in that the values are reordered consistently into a 1D array. At first glance, it seems reasonable to simply do a Euclidean distance style comparison of two of these arrays to get a...

Homework Statement I'm trying to find a natural definition for V[X|Y], but I'm not sure what a natural definition is. Any help?

Homework Statement Given a 30% failure rate, what is the mean number of students who fail, and what is the variance? There are 8 students in the course. Homework Equations I think these are the correct equations: Mean = Probability * Number of students Variance = Sum from i=1 to 8 of...

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 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...