Variance Definition and 357 Threads

<Moderator's note: Moved from a technical forum and thus no template.> So, I have this problem and I am stuck on a sum. The problem I was given is the following: The probability of a given number n of events (0 ≤ n < ∞) in a counting experiment per time (e.g. radioactive decay events per...

Suppose ##X## ~ N(##\mu##,##\sigma^2##). Then ##\bar{X}## ~ N(##\mu##,##\frac{\sigma^2}{n}##), where ##\bar{X}## is the random variable for sample mean for samples of size ##n##. But when the population variance ##\sigma^2## is unknown and the sample size ##n## is small, ##\bar{X}## no longer...

Homework Statement [/B] ##-1\leq\alpha\leq 1## ##f(y_1,y_2)=[1-\alpha\{(1-2e^{-y_1})(1-2e^{-y_2})\}]e^{-y_1-y_2}, 0\leq y_1, 0\leq y_2## and ##0## otherwise. Find ##V(Y_1-Y_2)##. Within what limits would you expect ##Y_1-Y_2## to fall? Homework Equations N/A The Attempt at a Solution...

Hello all, I have an interesting question regarding contribution margin (CM) % variance and how to attack it mathematically. If not known, contribution margin is defined as gross revenues minus all variable costs. This amount effectively shows how much money you have left to 'contribute' to...

Homework Statement A particle is moving in a one-dimensional harmonic oscillator, described by the Hamilton operator: H = \hbar \omega (a_+ a_- + \frac{1}{2}) at t = 0 we have \Psi(x,0) = \frac{1}{\sqrt{2}}(\psi_0(x)+i\psi_1(x)) Find the expectation value and variance of harmonic oscillator...

Hi, I'm hoping someone can point me in the right direction please. I'm using the Planck 2015 CMB temperature (intensity) SMICA pipeline maps (Nside = 2048) and am trying to determine the temperature variance of each individual pixel. Variance and hit-count were provided with the 2013 CMB maps...

Homework Statement for randomly selected IQ adult scores are normally distributed with mean of 100 and standarrd deviation of 15 ,. a sample of 24 randomly selected professors resulted in the IQ scores having a standard deviation of 10 . Test the claim that the IQ scores for the professors is...

Hello, I was reading an example where correlation between two features is to be measured. The two features are drive-wheels and price. The drive-wheels feature has three values: 4wd, fwd, and rwd. Then the example went on to calculate the F-score without much details using Python. Without going...

Homework Statement with an individual lines at its various windows , a post office finds that the standard deviation for normally distributed waiting times for customers on Friday afternoon is 7.2 minutes . The post office expreiemets with a single, main waiting line and finds that for a random...

Homework Statement "The mean pH value of a certain chemical is to be controlled at ##\mu = 5##. Deviation from this target value in either direction is to be detected with high probability. For this purpose it is proposed to measure a ceratin number of samples from each batch and decide that...

Homework Statement The distance between the Sun and the Earth varies during the year: it is a minimum in January, and about 3.3% larger at its maximum in July. What is the corresponding change in the Earth's effective temperature? Homework Equations Energy absorbed: $$ E_{abs} = \pi R^2 (1-...

From linear model, $y = X\beta + \epsilon$, if $\hat{\sigma}^2 = \frac{|y - Xb|^2}{n-p}$ is the variance of error and $\hat{\sigma}_{-i}^2 = \frac{|y_{-i} - X_{-i}b_{-i}|^2}{n-p-1}$ is the estimate of the error variance σ obtained by fitting all the observations except the i-th. Show that...

This is from labwork experiments. I have no background in mathematics. We have an experimental setup that measures the levels of two targets: The Reference (R) and the target of Interest (I). We are interested in the ratio I/R. For healthy individuals we know this ratio to be precisely 1. For...

In obtaining the Press Schechter function, the variance on mass scale is differentiated with respect to mass. The variance on a mass scale is a function of wavenumber k through the Power spectrum and transfer function. To eliminate k dependence, some value of k must be inserted into the...

For using Galilean transformation, I have to assume that speed of light w.r.t. ether frame is c. W.r.t. ether frame, E = E0 eik(x-ct) W.r.t. S' frame which is moving with speed v along the direction of propagation of light, E' = E0 eik(x'-c't') Under Galilean transformation, x' = x-vt, t' = t...

<This thread is a spin-off from another discussion. Cp. https://www.physicsforums.com/threads/wedge-product.914621/#post-5762138> Also again, be warned about this sloppy notation of indizes. You should put the prime on the symbol (or in addition to the symbol). Otherwise the equations don't...

Homework Statement I have a variable ##s_i## with probability distribution ##w(s_i)## ##(\Delta(s_i))^2## denotes the variance ##=<(s-<s>)^2>=<s^2>-<s>^2## I want to show ## \sum\limits_{i\neq j} <\Delta s_i> < \Delta s_j> =0 ## where ## < > ## denote expectation My book has: ## <\Delta...

Hi, I am studying about F ratio and how, as a random variable, it follows F Distribution. So let me explain what confuses me. This is what the theory says -- We draw two random samples $sample_x$ and $sample_y$ from two different Normally distributed populations with equal variance...

Have been reading about cepheid. Can I just check I've got this? 'When at their hottest (when gravity has squashed them) have more doubly ionised He so star becomes more opaque' Now was just wondering what the main mechanism is here? Because He2+ doesn't have any electrons left to absorb photons...

I did not understand of the non-existence of variance. What does it mean?

Homework Statement Let Y_1,Y_2 be independent random variable with uniform distribution on the interval [1,2]. Define X=max{Y_1,Y_2}. Find p.d.f., expected value and variance. Homework EquationsThe Attempt at a Solution Since $X=\max\{Y_1,Y_2\}$, this tells $Y_1$ and $Y_2$ must at most $x$...

Dear forumers, In advance, thank you for reading this post and helping me solving this. The problem is the following : I have a population (say, a bag) from which i take 3 samples. Each sample gets analysed once by a laboratory in order to know their concentration of a product. The result...

Homework Statement In this problem we will be generating and analyzing lists of normally distributed random numbers. The distribution we are sampling has true mean 0 and standard deviation 1. If we sample this distribution N=5 times, what do we expect the mean to be? How about the standard...

1. Homework Statement Not sure if this is the right place to post this, but I'm really confused about what is going on here. Any sort of breakdown of the mathematical operations for each step would be incredibly helpful. Homework Equations The ones given in the photo, not sure how to type...

I'm studying CFD and I'm on turbulence. It states that the fluctuating part of velocity squared and time averaged is the variance but variance in statistical terms is the deviation from the mean squared and averaged. So what is variance in turbulent fluctuating velocity? This variance is also...

HI, I need to calculate the variance of mass released when a particle jumps down or up between energy levels inside a black hole , i don't know where to begin any advice will help thanks

Homework Statement \textbf{The Logarithmic Series Distribution}. We will examine the properties of a the Logarithmic Series Distribution. We will check that is is a probability function and compute a general term for factorial moments and, hence, compute its mean and variance. This distribution...

Often in empirical studies you see statements that factor X explains some fraction of the variance in some other variable V, and thinking about what this means intuitively made me curious about the following question. Suppose you have a model where the values of some set of factors X1, X2, ...

Struggling with a problem dealing with %'s and how to determine the contribution that each element has to the total variance between 2 periods. Sorry, not sure if there is a way to embed excel spreadsheet into post so included snapshot with my questions/comments. Rate = Commission / Market

Homework Statement You buy 15 boxes each containing 4 microprocessors. All microprocessors come from a very large lot in which 9.5 % of microprocessors are defective. Y = the number of boxes in which there is less than 2 defective microprocessors. QUESTION: Find the Variance of the variable Y...

Homework Statement If you blow across the top of an empty soft-drink bottle, a pulse of sound travels down through the air in the bottle. At the moment the pulse reaches the bottom of the bottle, what is the correct description of the displacement of the elements of air from their equilibrium...

Homework Statement Weight of the plums of a large lot is averaging 70 g and SD 0.85 g. X= the average weight of plums in a pack of 14 plums. Find the variance of the variable X. Homework EquationsThe Attempt at a Solution n=14 Average_Total= 70*14=980 SD2 = Variance_Total= 0.852 *12 = 10.115...

It should be noted that this is not homework but rather practice for an exam. Is this the place I should be asking these types of questions? Homework Statement An apple is held completely submerged just below the surface of the water in a container. The apple is then moved to a deeper point in...

Homework Statement https://dl.dropboxusercontent.com/u/17974596/Sk%C3%A6rmbillede%202016-02-02%20kl.%2007.35.26.png I want to find variance matrix and expected variance vector of Y=(Y1,Y2). Y1 and Y2 are independant. Γ is the gamma function and ϒ is a known parameter. λ1>0 λ2>0 and ϒ>0...

0http://stackoverflow.com/questions/34833391/tannor-quantum-mechanics-derivative-of-variance-of-position# In the Tannor textbook Introduction to Quantum Mechanics, there is a second derivative of chi on p37. It looks like this: χ"(t) = d/dt ( (1/m) * (<qp + pq> - 2<p><q> ) (Equation...

Hello everyone, I'm stuck at a elementary stochastic problem. I have to calculate means, variance and co-variance for two random variables. Homework Statement Let r,g,b∈ℕ. r red, g green and b black balls are placed in an urn. The balls are then drawn one at a time with replacement, until a...

Why do people say that RVs that have the normal distribution has a constant variance. What does that mean constant variance.

In a Quantum Mechanics Class, my tutor had shown me that the variance Δa2 Δa2 = < ( a - < a > )2 > = < a2 - 2 a < a > + < a >2 > = < a2 > - 2 < a >< a > + < a >2 = < a2 > - 2 < a >2 + < a >2 = < a2 > - < a >2 and my questions are i) why, in step 3, < x - y + z > will become < x > - < y > + <...

Homework Statement find μ and σ^2 for the following probability density f(x) = x for 0<x<1 f(x) = 2-x for 1 <= x < 2 f(x) = 0 elsewhere Homework Equations μ = ∫xf(x)dx σ^2 = ∫x^2 f(x)dx - μ^2 The Attempt at a Solution first we find the mean. we split up the integral into sums of different...

Suppose X and Y have the same distribution, and Corr(X,Y) = -0.5. Find V[X+Y]. I know that Corr(X,Y)*SD[X]SD[Y] = Cov(X,Y) and also V[X+Y] = V[X] + V[Y] + 2Cov(X,Y) So there must be a missing link, maybe an identity, that I'm not realizing. I think the fact that the 2 variables have the same...

Homework Statement Work out the variance of momentum in the infinite square well that sits between x=0 and x=aHomework Equations Var(p) = <p2> - <p>2 $$ p = -i\hbar \frac{{\partial}}{\partial x} $$ The Attempt at a Solution I've calculated (and understand physically) why <p> = 0 Now I'm...

The below is motivated by a problem I'm observing in my experimental data I have m boxes, where each box is supposed to contain k molecules of mRNA. The measurement process includes labeling all the molecules with a box-specific tag, mixing them, amplifying them to detectable levels and...

See the photo of the question+ mark scheme! I don't understand a question on finding an expression for the variance of something... Attempt at solution: also I worked out c as (3/2) previously, which is correct Var(U) = (3/2)^2 x Var(Xbar) = 9/4n^2 x a^2/18 I'll attach a photo of this too if...

Dear all, I'm not a mathematician so please excuse me for a certain lack of strictness ... I work on random signals in physics, these signals are most of the time called "noise" for us. For example, we can speak about x(t), a time domain random signal. Very usually, the statistics...

If I have three sets of numbers A is numbers between 0 and 0.09 B is numbers between 0.091 and 0.011 C is numbers between 0.011 and 0.1 where the number of elements in A are say, 37, B are 16 and C are 178. So the three arrays have different numbers of points and different distances, plotting...

Homework Statement ti[/B] A resistance thermometer, which measures temperature by measuring the change in resistance of a conductor, is made of platinum and has a resistance of 50.0 Ohms? at 20.0°C. (a) When the device is immersed in a vessel containing melting indium, its resistance increases...

When we try to find the statistical correlation of some perturbation between two positions, we always calculate the quantum 2-point function. Are these two concepts really the same? Also, people say vacuum fluctuation is gaussian. For normalized fields, we always use Bunch-Davies initial...

I am trying to use a generated random sample in R to estimate the mean and variance for a Poisson random variable. The first one is a Poisson random variable with mean 5. To estimate the above I generate a random sample in R with the following code: P5 <- rpois(100,5) Given the above I want to...

Hello all, I have this question, which I think I partially knows how to solve, but need some completion. "A man is playing versus a machine in the following way: The machine chooses 2 numbers randomly from the set of numbers 1,2,3,4,5, where a number can be chosen twice (with replacement). If...

Hi, i am trying to find the variance of the following: y*(s+n), where y is a m \times 1 vector following a chi-squared distribution with 2k degrees of freedom, s is a m \times 1 vector following a Gaussian distribution with zero mean and unit-variance, and n is a m \times 1 vector following a...