Variance Definition and 329 Threads

Homework Statement Given that 8 person vote for Mr Tan , i can't understand why the probability is sum of 0 people vote for him until 8 people vote for him. Why not the probability = 22c8 ( (0.6)^8 )( (0.4)^14) ? Homework EquationsThe Attempt at a Solution

$$\text{Consider the following decomposition of the time series }{Y}_{t}\text{ where }{Y}_{t}={m}_{t}+{\varepsilon}_{t},\text{ where }{\varepsilon}_{t}\text{ is a sequence of i.i.d }\left(0,{\sigma}^{2}\right)\text{ process. Compute the mean and variance of the process }{\nabla}_{2}{Y}_{t}\text{...

Ok, so I got this question on an exam some time ago and I still don't understand why I didn't get it (I can't remember the exact question, but this is very similar): "A lottery winning amount is determined in the following manner: first a die is thrown. If the result is 1 or 2, the lottery...

Hello! I'm not entirely sure this is very "scientific", but I have an idea that I would like some feedback on. I remember reading an article related to radioactive decay varying with the rotation and distance from the sun on Phys.org a few years back (http://phys.org/news202456660.html) and was...

Homework Statement This is a statistics as applied to astronomy problem. My stats knowledge is horrible. Anyway, the problem: For several hundred objects, I have a number of different properties for which I have a measurement & associated measurement error. For example, flux density and...

Homework Statement Math and verbal SAT scores are each N(500, 10000) 1)If the math and verbal SAT scores were independently distributed, which is not the case, then what would be the distribution of the overall SAT scores? Find its mean and variance. Homework Equations The...

I am trying to derive the Probability distribution of Geometric Brownian motion, and I don't know how to find the variance. start with geometric brownian motion dX=\mu X dt + \sigma X dB I use ito's lemma working towards the solution, and I get this. \ln X = (\mu - \frac{\sigma...

hello again pf! as a really simple question, can someone talk to me about the difference between variance and kurtosis? i know as kurtosis decreases from 3 (normal distribution) our pdf is shorter and fatter, with less weight in the tails. i also know variance tells us how dispersed data is...

I'm reading a journal article that implies the following but I can't see how it is done. I'll give 100 DogeCoin (or equivalent) to whomever can explain this in full. Given that V(A|B) = s V(A) = r*s + w B = A + C and A & C are independent so V(B) = V(A) + V(C) & V(C) = V(B) - V(A) Then how...

Hi there. I would like to ask you one question about variance of estimator. Suppose that Y_i=βX_i+ε_i and β estimator is \bar{Y} / \bar{X}. I calculated mean of estimator. I am not sure if it's correct, but i got that its equal to n*β. But how about variance. Any help would be appreciated!

Homework Statement 1. Assume each birth in a hospital on a given day is independent of one another, and each birth, P(boy)=0.48. What is the probability that the 8th baby born is the 5th girl. 2. Two random variables X and Y have joint distribution given by. What is their correlation. 3. Z...

Distributions: sample mean and variance, and variance of sample means? Hi. Say you have a population, and from there you can draw a stochastic variable ##X## with a specified distribution. So you take out a few sizeable samples from the population, and calculate the mean and variance of ##X##...

Homework Statement I am attempting to calculate a heat transfer across a medium with known material properties. I have the equation and all but one variable I have an exact answer for. I require the variance of my answer. Homework Equations I know ALL variables (ie numerical value) except...

Hi everyone, hopefully someone can help For an vector AR(1) model of the form y(t)=Ay(t-1) + et How does one estimate the variance of the white noise input. I was under the impression that one can simply use the residual of the model fit and estimate the variance from this, when I do a...

Homework Statement A coin is flipped repeatedly with probability p of landing on heads each flip. Calculate the average <n> and the variance \sigma^2 = <n^2> - <n>^2 of the attempt n at which heads appears for the first time. Homework Equations \sigma^2 = <n^2> - <n>^2 The...

Ive been stuck at this question for over 5 hours now trying to figure out what the answer is. Please help!:confused: We have observed 250 cars on a motorway with speed limit of 90 km/h Speed number of cars 75 32 85...

Homework Statement Consider the sphere x2 + y2 + z2 = 1 Find the mean and variance. Homework Equations The Attempt at a Solution Mean = 0 (Symmetry) Variance Probability = \frac {dV}{\frac{4}{3} \pi R^3} = \frac {4 \pi r^2 dr}{\frac{4}{3} \pi R^3} = 3 \frac {r^2}{R^3} dr Variance =...

Homework Statement For the nonparameteric estimator \hat{f}(x)=\frac{1}{2hn}\sum\limits_{i=1}^n I_i(x) of a pdf, (a) Obtain its mean and determine the bias of the estimator (b) Obtain its variance Homework Equations The Attempt at a Solution For (a), I think it goes like this...

Quantum mechanics has a well-known procedure for evaluating the expectation value of an observable quantity in a given quantum state. First one must obtain the quantum operator O that is associated with the observable quantity. Then the rule for computing the expectation value is: Apply O to the...

Homework Statement Suppose that: E(X1) = μ, Var(X1) = 7, E(X2) = μ, Var(X2) = 13, E(X3) = μ, and Var(X3) = 20, and consider the point estimates: μˆ1 = X1/3 + X2/3 + X3/3 μˆ2 = X1/4 + X2/3 + X3/5 μˆ3 = X1/6 + X2/3 + X3/4 + 2 (a) Calculate the bias of each point estimate. Is...

Hi there , I have some simple (on 1st look) questions. I just need some help.http://img59.imageshack.us/img59/3018/5hby.png 1st question. I think the expected value should be 150 since the probability of getting a head is 1/2 .. 300x1/2 = 150 so the mean should also be 150. the variance...

Homework Statement Not exactly a homework question, but rather a section in Statistical Data Analysis: Suppose there is a pdf y(x)[/SUB] that is not completely known, but μi and Vij are known: Homework Equations The Attempt at a Solution I understand how <y(x)> ≈ y(μ), My confusion: Why...

X ~ standard uniform random variable We toss a coin randomly and define Y := { X if the coin toss is heads ...{ 1 is the coin toss is tails Question wants the Var(Y^p) for any p > 0. My work: Var(Y^p) = E(Y^(2p)) - E(Y^p)^2 I'm not sure how to go about finding E(Y^p) and E(Y^(2p)). I thought...

f(x)=f(x)={█(2/(√2π) e^(〖-x〗^2/2)@0 otherwise)┤for 0<x<∞ Find the mean and variance of X The hint says, compute E(X) directly and then compute E(X2) by comparing that integral with the integral representing the variance of a variable that is N (0, 1)

I have attached the problem of interest. I think I am having trouble calculating the standard deviation for part a. D=A-B-C E(A)=10 E(B)=2 E(C)=2 sigma(A)=0.1 sigma(B)=0.05 sigma(C)=0.1 where sigma=standard deviation so to find SD...

Homework Statement Showthe two forms of the sample variance are equivalent: \frac{1}{n-1}\sum_{i=1}^\n (Yi-Ybar)2 = \frac{1}{n(n-1)}\sum_{i=1}^\n \sum_{j>i}\n (Yi-Yj)2 The first summation is from i=1 to n, the second is i=1 to n and the third is j>i to n. Sorry, I don't know how to format...

Could someone please explain it to me what is the difference between Variance and Covariance?

Hi all, For finding average we take the sum of sequence numbers and divide by the number of elements. Why for variance this changes to number of elements minus 1. -Devanand T

Hi, friends! Since this is my first post, I want to present myself as an Italian who is trying to teach himself mathematics and natural sciences, while having a strictly humanities-centered school background, and I am tempted very much to enrol in a university scientific course. I read in the...

Hi all, Note: The text below is the motivation for my question. To jump to the question immediately, please skip to the line that says HI! I have a set of data points, let's call it A, and I ran principal component analysis to get the top 3 principal components to be able to represent the...

1) For the normal distribution it seems that the integral of the propability density function from \mu-\sigma to \mu+\sigma is independent of \sigma. I guess that gives kind of a nice interpretation of \sigma. But how do you prove this, when the antiderivative of an exponential with a square...

I saw an equation on wikipedia: (http://en.wikipedia.org/wiki/Fermi-Dirac_statistics) Does anybody know how this is derived?

day 1 distance equals 52.175m, std = 0.015m and n = 10 day 2 distance equals 52.193m, std = 0.021m and n = 11 Establish whether the two populations have equal variance at the 0.05 signifcance level. Can someone help me out with how to get to the answer and what the answer actually is?

Moment generating functions: How can I show that Var(X)=\frac{d^2}{dt^2}ln M_X(t)\big |_{t=0} Recall: M_X(t)=E(e^{tx})=\int_{-\infty}^{\infty}e^{tx}f(x)dx E(X^n)=\frac{d^n}{dt^n}M_X(t)\big |_{t=0} Var(X)=E(X^2)-[E(X)]^2=E[(X-E(X))^2] ------------ I tried just applying the equation...

Homework Statement The time it takes for a nurse to look up a patient journal is uniformly distributed between three and seven minutes. One morning there's 96 journal orders for the nurse to take care of. Calculate the probability that she will get them all done during an eight hour work...

Let X1, X2, X3 be three random variables. Suppose all three have mean μ and variance 1. The sample mean is Y = (X1 +X2 +X3)/3. (a) Can you compute the mean of Y? If so, what is it? If not, why not? I have that it is either μ OR that it is not possible to find, since we don't know if they...

Homework Statement Measure of Contaminatino has a normal distribution w/ unknown mean and unknown variance. Random sample of n=40 provides sample mean = 28.30 and sample variance = 17.38 1)Find Upper 95% Confidence Interval 2)Test Null Hyp = 25.5 vs Alt Hyp = 28.30... Upper Tailed...

The random variable X1, X2,...,X15 are independent and take each values ​​ +1,-1 with probability 1/2. We define Y = sum from j=1 to 15(j*Xj) whats is the variance VAR(Y)=? i will find this with VAR(Y)=E(X^2)-(E(X)^2) but how i can find them?

The variance is denoted by σ^{2} It is calculated with this equation: [SIZE="4"]σ^{2}=\frac{\sum^{N}_{i=1}(Xi-μ)^{2}}{N} Which makes sense. To calculate the average (deviation from the mean)^2 you need to sum up the (deviations from the mean)^2 and then divided by the number of deviations...

Hello I have a problem solving this question... to the numbers 0 and 2, we want to add a 3rd number, such that the variance won't change. What is the 3rd number ? (when I say variance I mean dividing by n, not by n-1) thanks !

First of, I apologize for the vague title, I didn't know how to summarize this issue. Homework Statement Suppose that the interest rate obtained in month i is a random variable Ri with the uniform distribution on [0.01, 0.03], where R1,R2, . . . are independent. A capital of 1 unit...

Hello, Any help with this one would be appreciated. In a college 80 students are taking the exam in the spring semester. Their grades has a mean and standard deviation. In the summer semester, k additional students are being tested. All k students get grades which are equal to the average...

Hi, I'm trying to create a normal distribution with mean 0.5 and variance 0.05. I tried it initially with MATLAB, for which I used newdist=0.5+(randn(1,1000)*sqrt(0.05)); Could you please help me in doing this in FORTRAN 90? Would generating a sequence using RANDOM_NUMBER and using the...

Homework Statement Which of the following formulas represents the variance of the data set {x1,x2,x3,...,x10}? (μ denotes the mean of the data set) Here is a photo that I took of the problem for better understanding. http://i.imgur.com/PqEKajx.jpg?1?7734 I understand why the answer I chose...

Homework Statement For every bike that comes into a repair shop there is a 0.1 probability that a wheel will need replacing. The shop always has 3 wheels in stock. X is the number of bikes that can be repaired before the wheels run out. I need to figure out the mean and variance of X...

Does μx mean the same thing as E[X]? Also, does σ2x mean the same thing as Var X?

Homework Statement Im working on this data set, and I can't get the "Grand Variance" calculated correctly, driving me nutz! So, its 3 groups of data. Group 1 mean = 2.20 group 2 mean = 3.20 group 3 mean = 5 Group 1 variance = 1.70 Group 2 variance = 1.70 Group 3 variance = 2.50 Now, it...

Just a thought experiment. Imagine you made scale models of the sun and the planets with the relational standard of measure being a sun the size of a basketball. Now assume that the sun and the planets were all built to scale with the appropriate diameters, densities and masses of the actual 8...

Homework Statement Suppose the distribution of X2 conditional on X1=x1 is N(x1,x12), and that the marginal distribution of X1 is U(0,1). Find the mean and variance of X2. Homework Equations Theorem: E(X_{2})=E_{1}(E_{2|1}(X_{2}|X_{1}))...

I am trying to investigate the statistical variance of the eigenvalues of sample covariance matrices using Matlab. To clarify, each sample covariance matrix, \hat{\mathbb{R}}_{nn}, is constructed from a finite number, N, of vector snapshots, each sized (L_{vec} \times 1) (afflicted with random...