In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its mean. In other words, it measures how far a set of numbers is spread out from their average value. Variance has a central role in statistics, where some ideas that use it include descriptive statistics, statistical inference, hypothesis testing, goodness of fit, and Monte Carlo sampling. Variance is an important tool in the sciences, where statistical analysis of data is common. The variance is the square of the standard deviation, the second central moment of a distribution, and the covariance of the random variable with itself, and it is often represented by
Hello,
I would like to know the right expression for the expression of variance of Shot noise in spectroscopic probe.
Sometimes, I saw ##\sigma_{SN,sp}^{2} = 1/n_{sp}## with ##n_{sp}## the average density of galaxies, whereas my tutor tells me that ##\sigma_{SN,sp}^{2} = 1/n_{sp}^{2}## , so I...
In the context of Survey of Dark energy stage IV, I need to evaluate the error on a new observable called "O" which is equal to :
\begin{equation}
O=\left(\frac{C_{\ell, \mathrm{gal}, \mathrm{sp}}^{\prime}}{C_{\ell, \mathrm{gal}, \mathrm{ph}}^{\prime}}\right)=\left(\frac{b_{s p}}{b_{p...
Below the error on photometric galaxy clustering under the form of covariance :
$$
\Delta C_{i j}^{A B}(\ell)=\sqrt{\frac{2}{(2 \ell+1) f_{\mathrm{sky}} \Delta \ell}}\left[C_{i j}^{A B}(\ell)+N_{i j}^{A B}(\ell)\right]
$$
where ##_{\text {sky }}## is the fraction of surveyed sky and ##A, B##...
Hello everyone.
I have two points in space (on the surface of the earth) represented using spherical coordinates (in this case there is no z axis since both are assumed to be at the same height). These points have an associated standard deviation in lambda and in phi, which are longitude and...
In a paper published in the JOURNAL OF MATHEMATICAL PSYCHOLOGY 39, 265-274 (1995), formulas are provided on page 272 for the expectation E(Tn) of a random variable T as dependent on n (formulas 28 and 29). Now I would like to know what these formulas look like for the variance i.e. Var(Tn).
Hello everyone. I am currently using the pca function from matlab on a gaussian process. Matlab's pca offers three results. Coeff, Score and Latent. Latent are the eigenvalues of the covariance matrix, Coeff are the eigenvectors of said matrix and Score are the representation of the original...
A coin had tossed three times. Let ##X##- number of tails and ##Y##- number of heads. Find the expected value and variance ##Z=XY##.
My solution:
We know, that ##Y=3-X##, so ##Z=(3-X)X## for ##X=0,1,2,3##.
##Z=2## for ##X=1,2## and ##Z=0## for ##X=3,0##
So, ##E(Z)=E((3-X)X))= 2 \cdot ⅜ +2 \cdot...
Homework Statement
[/B]
For reference:
Book: Mathematical Statistics with Applications, 7th Ed., by Wackerly, Mendenhall, and Scheaffer.
Problem: 10.81
From two normal populations with respective variances ##\sigma_1^2## and ##\sigma_2^2##, we observe independent sample variances ##S_1^2## and...
Problem:
We play roulette in a casino. We watch 100 rounds that result in a number between 1 and 36. and count the number of rounds for which the result is odd.
assuming that the roulette is fair, calculate the mean and deviation
Solution:
I understand that the probability - Pr = 0.5. and...
Homework Statement
For a wavefunction ##\psi##, the variance of the Hamiltonian operator ##\hat{H}## is defined as:
$$\sigma^2 = \big \langle \psi \mid (\hat{H} - \langle\hat{H}\rangle)^2 \psi \big\rangle$$
I want to prove that if ##\sigma^2 = 0##, then ##\psi## is a solution to the...
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...
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
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...
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, ...
0http://stackoverflow.com/questions/34833391/tannor-quantum-mechanics-derivative-of-variance-of-position# [Broken]
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> )...
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
Find the variance of Y=3x^2+3x+3
The Attempt at a Solution
Let Y = 3x^2 +3x +3
Var(Y) = Var(3x^2 +3x +3) = 9Var(x^2) +9Var(x) = 9 [E[X^4] - E[X^2]^2 +E[X^2] - E[X]^2]
This is wrong.
Using a normal approximation method for the Wilcoxon Signed-Rank Test, I've seen that the expected value is \mu = \frac {n(n+1)}2 and the variance is \sigma^2 = \frac {n(n+1)(2n+1)}{24} .
I'm wondering why these are the expected value and variance.
I do recognize the formula for the sum of...