Questions tagged [variance]
For questions regarding the variance of a random variable in probability, as well as the variance of a list or data in statistics.
0
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0answers
4 views
Choosing between two unbiased estimators - working out the Variance correctly
I am given the random sample X1, . . . , Xn, which is identically and independently distributed over f(X), for a population density f(X) with finite mean μ and variance $σ_2$. I am given the estimator
...
-1
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0answers
16 views
What is the maximum possible variance for a collection of N numbers ranging from 0..X? [on hold]
For an collection of N numbers, all ranged from zero to X, what is the maximum possible variance of the collection for given N & X?
-1
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0answers
10 views
Conditional expectation and variance for beta RV
A random variable X has the Beta($\alpha$,$\alpha$+ 1) distribution, with $\alpha$ > 0. The parameter $\alpha$ itself is random, and can take the values 1 or 2, with probabilities 1/2 each. Compute E(...
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2answers
26 views
Having the sum of the squares, get the squares of the subtraction
I have to calculate this:
$$S^2=\frac{1}{n-1}\sum_{i=1}^n (X_i-\mu)^2$$
But I have $n$, $\mu$ and the sum of the squares of $X_i$. In other words: $\sum_{i=1}^n X_i^2$.
How can I calculate $S^2$?
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0answers
20 views
Mathematical derivation of why Bagging reduces variance
I am having a problem understanding the following math in derivation that bagging reduces variance. The math is shown but can not work it out as some steps is missing. link
-1
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0answers
21 views
Probability, expectations [on hold]
i need help with this exercise. (I google translated from norwegian so sorry if the english is bad)
We want to find the proportion of the working population that is unemployed at some point.
A ...
1
vote
2answers
62 views
is this true: Var(|X|) ≤ Var(X)? [closed]
I am trying to decide whether $$\text{Var} (\lvert X \rvert) \le \text{Var}(X)$$ is true. I am getting stuck because I don't know if $$E^{2}[ \lvert X \rvert ] \gt E^{2} [ X ]$$
-4
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1answer
36 views
Why is $E[(X − b) ^2 ]$ minimal when $b = µ$? [closed]
If $X$ is a random variable with a mean µ and a variance $σ^2$, why is $$E[(X − b) ^2 ]$$ minimal when $b = µ$?
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0answers
44 views
Covariance matrix and projection
I have troubles understanding a geometrical meaning of a covariance matrix.
Let's say we have a data set containing two points (-1,1), (-1,2) and write them in to the matrix
$$D = \begin{bmatrix}
-...
0
votes
1answer
28 views
Hypothesis testing variance using sample mean
I know how to test hypotheses for variance using methods like the chi-square test.
However, this problem is asking me to use a rejection region construction in terms of the sum of the sample values (...
1
vote
1answer
9 views
Variance of combination of Brownian Motions
Let $Z(t)=W(t)-\frac{t}{T}W(T-t)$ for any $0\leq t\leq T$ with $W(t)$ a Brownian motion, find the variance of $Z(t)$.
My attempt:
$Var(Z(t))=\mathbb{E}(Z(t)^{2})-\mathbb{E}(Z(t))^{2}$
$Z(t)=W(t)-\...
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0answers
13 views
Help with a variance proof
I've been doing these exercises, but there is a proof (considering a binomial distribution of $n=4$, where $p$ is the probability of something happening, that has a median $m=4p$, prove, using the ...
1
vote
1answer
35 views
Basic Chi square problem
How do I calculate $P(S^2 > 1.8307(\mathrm{PopVariance}))$ if $n =11$?
I think I should use the Chi square formula:
$$X^2 = \frac{(n-1)s^2}{\mathrm{PopVariance}}$$
But I can't really understand ...
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votes
1answer
26 views
How can $\sigma^2$ be derived as a function of $\mu$ in a Gaussian pdf?
I have a Gaussian pdf defined as
$$f_X(x) =\frac{1}{\sigma\sqrt{2\pi}}\exp\left\{-\frac{(x-\mu)^2}{2\sigma^2}\right\}$$
whose $\mu = \frac{d^2}{6D}$, where $d$ is distance parameter and $D$ is the ...
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0answers
4 views
How to come up with variance for estimators?
I know that the variance is calculated with $Var(X) = \frac{1}{N} \sum^N (X_i - \bar{X})^2$
However, how do I come up with/derive variance formulas for e.g. the mean for different sampling methods.
...
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1answer
15 views
Dimensional properties derived from PCA eigenvectors
Background
Let's assume I'm using principal component analysis to carry out clustering of a 2-d data set, using a non-normalized covariance matrix to carry out the operation. I then solve for the ...
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0answers
15 views
How to calculate variance or diversity index in this chart
The bar shows an information regarding a team, in which 5 people know java, 10 know javascript etc How can I calculate diversity in this team, or perhaps the variance if in this case variance is same ...
-3
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0answers
52 views
A box contains 3 red balls and 2 white balls
A box contains 3 red balls and 2 white balls. Two balls are picked randomly from the box without replacement. The random variable 𝑿 is the number of red balls, and 𝒀 is the number of white balls.
...
0
votes
1answer
27 views
Are the mean and variance of a set equals the sum of its means and variaces
I'm not so fit in statistics and I found some controverse answers on the internet so I'm asking here.
I have a set $A$ with 10439 samples. The set is not of unique values and many of the sample ...
0
votes
1answer
14 views
What is the probability mass function of the measured voltage?
In a specific design, the true voltage of a circuit is 250 millivolt(mV). Measurement error that is continuous and uniformly distributed from -3 to +3 mV is added to the true voltage. the measurement ...
1
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1answer
39 views
Is it possible to calculate this special variance?
If i want to estimate the probability, that a random variable $X$ with any continuous distribution takes some value $>a$, i could estimate this with a sample from the correct distribution $X_1,...,...
2
votes
1answer
29 views
Variance of a Brownian motion
Let $\{X(t), t \geq 0\}$ be a Brownian motion with drift parameter $\mu = 3$ and variance parameter $\sigma^2 = 9$. If $X(0) = 10$, find $P(X(0.5) > 10)$.
First, I calculated the expectation and ...
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0answers
34 views
What is meaning of wavy arrow symbol and star symbol?
I have no idea with the wavy arrow symbol(yellow color) in this paper.
If anyone knows about this symbol, could you explain me?
And also I don't understand what is meaning of the STAR symbol in the ...
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0answers
11 views
Scalar product induced by covariance matrix
Suppose that $n$-dimensional random vector $Y$ has covariance matrix $\Sigma$. It is well known that for any $a\in\mathbb{R}^n$ we have
\begin{align}
var(a^TY)=a^T\Sigma a.
\end{align}
Is there any ...
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0answers
20 views
Variance and covariances from linear mixed model for power simulation using R
I am working with longitudinal data where the outcome is the number of steps per minute. My LMM fit would look like:
...
1
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0answers
46 views
Variance of sum of $m$ dependent random variables
Let $X_1,X_2,...$ be a sequence of identically distributed and $m$-dependent random variables with $\mathbb{E}[X_i]=0$, $0<Var(X_i)<\infty$ ($m$-dependent means that each $X_i$ is independent of ...
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votes
1answer
18 views
convergence almost surely implies convergence of variance?
Does $X_{n} \to X$ almost surely imply that $Var[X_{n}] \to Var[X]?$
I saw this post
convergence in mean square implies convergence of variance
which states that $X_{n} \to X$ in $L^{2}$ implies ...
0
votes
0answers
13 views
Adding variances of a variable
I have the average variance of a stock's daily return over a year and I want to know whether or not I can times this number by 252 (number of trading days in a year) to find the yearly variance. My ...
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0answers
5 views
Variance estimation of a secondary, non-observable variable
Sorry for lack of math rigor in advance. I want to estimate variance of a stochastic variable $Y$ that is only observable through a continuous, time limited function $f(t)$ as
$f(t+Y)$
Regarding $f(...
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1answer
34 views
Finding variance without the data
A researcher is testing the effectiveness of a political video. She has randomly sampled 120 people to test the video. For each person, there is 50% chance the person will be Democrat and 50% chance ...
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1answer
22 views
Regression model + expected value, variance and autocorrelation of the error term
Consider this regression model
$$Y_t=X_t\beta+\epsilon_t, ~~~~~~~~~~\epsilon_t \sim WN(0, \sigma^2_{\epsilon})$$
with 3 different specifications of the error term:
$\epsilon_t=\alpha_1\epsilon_{t-1}+...
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votes
1answer
14 views
MLE : Effect of incorrect variance on the mean for a normal distribution
Consider we have univariate samples, $x_k$, belonging to a category $\omega$ drawn from a dataset D according to an assumed distribution $p(x|\omega)$ $\sim N(\mu, 1)$. However, let the true ...
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0answers
13 views
Variance of truncated 2d Gaussian
To find the expectation of the Truncated Gaussian E($z_1^2$| $z_1^2 \leq \tau , z_2^2 \geq \tau$). Where $\boldsymbol{z} = [z_1,z_2]^T$ and $\boldsymbol{z} \sim \mathcal{N}(\boldsymbol{0},C)$, where $...
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0answers
18 views
Variance of double integral of changing error
I have the following case and would like to know if there is a better approach than the one I am currently following.
I have an array of errors ($\epsilon(i)$) and an array of corresponding variances ...
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1answer
16 views
Conditional Expectation of a Sum of Random Variables and a Random Integer
Let $(X_n : n \in \Bbb N)$ be a sequence of identically distributed random variables, with mean $ \mu$ and variance $\sigma^2 < \infty$. Set $S_0 = 0$ and $S_n=X_1+X_2+...+X_n$ for $n>0$. Let $N$...
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0answers
18 views
What is the minimum variance band of Poisson Distribution?
I am trying to calculate the minimum variance bound of Poisson Distribution.
poisson distribution: P(X=x)=(λ^x)/x! e^-λ,
were λ is the mean.
I got λ/(sum of x), but I am not sure if this is right.
...
0
votes
1answer
10 views
How to show that the error variance of the best linear predictor is inferior to the proportional predictor?
Let's consider the 1D case. How do we prove that the error variance of the Best Linear Predictor (BLP) is inferior than the Proportional Predictor (i.e. the Linear Predictor without the intercept)?
...
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2answers
40 views
About Conditional Variance $X$ Has distribution $ U(0,1)$ and $Y$ has distribution $ U(0,X)$
I have a question about the problem mentioned above, the main says
$X$ Has distribution $ U(0,1)$ and $Y$ has distribution $ U(0,X)$ Find $E(Y)$ and $Var(Y)$
I try to take it for $E[Y|X]=X$ and $...
6
votes
4answers
487 views
Variance of sine and cosine of a random variable
Suppose $X$ is a random variable drawn from a normal distribution with mean $E$ and variance $V$. How could I calculate variance of $\sin(X)$ and $\cos(X)$?
(I thought the question was simple and ...
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0answers
33 views
Show that T achieves the Cramer Rao lower bound
Problem Statement:
Consider $T$ to be an estimator of $\theta$.
Show that $T$ achieves the Cramer Rao lower bound if and only if $Z$ is a linear function of $T$
$Z=a(\theta)T+b(\theta)$ ...
1
vote
1answer
41 views
We have an urn with 6 red balls and 4 green balls.
We have an urn with 6 red balls and 4 green balls. We draw
balls from the urn one by one without replacement, noting the order of the
colors, until the urn is empty. Let X be the number of red balls ...
0
votes
1answer
14 views
$Y = \frac { K A ^ { 3 } } { ( B + D ) ( C - D ) }$
K is a constant
Find an expression to approximately determine the variance of Y, assuming $A , B , C ,$ and $D$ are probabilistically independent.
isnt the expression they have already given me the ...
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votes
1answer
37 views
Minimum variance of $k_1X+k_2Y$ where $X,Y$ are independent Poisson
I have the following question for homework:
Suppose that $X$ and $Y$ are independent Poisson distributed values with means $\theta$ and $2\theta$, respectively. Consider the combined estimator ...
2
votes
2answers
73 views
Variance and mean of balls in bins limited capacity
Let there be $m$ indistinguishable balls, $k$ bins, $C$ capacity.
Let $X_j$ denote the total balls in bin $j$.
I've seen ways to calculate the total number of combinations, but I'm not sure how to go ...
1
vote
2answers
24 views
A random variable $X$ is number of boys out of $n$ children. Calculate $\operatorname{Var}(2X-n)$
Let a random variable $X$ be the number of boys out of $n$ children. The probability to have a boy or a girl is $0.5$. Calculate $V(2X-n)$.
I know that $Var(2X-n)=4V(X)$.
$\mathbb{P}(X=k)={1\over 2^...
0
votes
2answers
34 views
Formula to recalculate Variance after removing a value and adding another one given old variance
Let's say I have a data set of $10,20,30$. My mean and variance here are mean= $20$ and variance = $66.667$. Is there a formula that lets me calculate the new variance value if I was to remove $10$ ...
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1answer
17 views
Partial permutation of time sequence data that keep order of events
Suppose you have sequence S of N elements that are descending ordered by time. How many ways can you take K element subsets from S preserving time descending ordering?
example for sequence S={A,B,C,D,...
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0answers
6 views
How to find the most suitable cutoff of a function to calculate its vertical variance?
I have say a function $y=f(x)$ below that tends to $a$ and $b$ at the infinites. I want to calculate its vertical variance $\text{Var} [y]$ of the interesting part in the middle. If I calculate for ...
0
votes
1answer
49 views
Variance of sum of weighted gaussian random variable
This problem comes from section 3.2. at page 7 of this paper
Suppose there are $N$ independent gaussian random variables $z_1,z_2,z_3,...,z_N$. That is
$$z_i \sim N(\mu _i,\sigma _i^2).$$
Now let
$$z=\...
1
vote
3answers
77 views
What is the largest possible variance of a random variable on $[0; 1]$?
What is the largest possible variance of a random variable on $[0; 1]$?
It is evident that it does not exceed $1$, but I doubt, that $1$ is actually possible. The largest variance, for which I found ...
