Questions tagged [sum]
The sum of two or more random variables.
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Estimating the distribution of a sum of two random variables if the family of one of the variables is known
Assume I have a random variable $Y=X_1+X_2$. I want to estimate the distribution $f$ of $Y$ given a sample $y_1,\ldots,y_N$. If this was all that is known about $Y$ the best way would probably be to ...
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Estimating the probability of a sum of events
I have n machines that use the same utility. Each machine randomly demands a unique f_n flow rate of the utility once every h_n hours on average. Each machine's demand event lasts for about m_n ...
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Noise cancels but variance sums - contradiction?
I have been told both things with regard to e.g. summing noisy time series, to justify opposing expectations.
On the one hand, I have been told to expect that summing multiple noisy inputs should lead ...
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How to rewrite a multivariate polynomial term without redundancies?
This is from an exercise found here on page 60. My question is: what is meant by $\sum\limits_{i_1=1}^D\sum\limits_{i_2=1}^{i_1}...\sum\limits_{i_M=1}^{i_{M-1}}w_{i_1i_2...i_M}x_{i_1}x_{i_2}...x_{i_M}$...
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Summing multiple standard deviations (repeated measures) [duplicate]
Say a set of 5 participants completed two subtests (A and B). The scores on these subtests can be summed to get a total test score. Here is the dummy data:
Participant
Subtest A
Subtest B
Total test
...
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Model Sum of Squares from ANOVA table
Background: I am studying a course on statistical experiments using the textbook by Douglas Montgomery on the analysis of experiments. This is an introductory course and so I am relatively new to the ...
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Given a set of random variables, how can I find a linear combination of these variables satisfying a constraint on the sum of their permuations?
Say I have n random variables, {X0...Xn}, n>9. I also have another set of random variables constructed from the first set, where each of these are the sum of 9 ...
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How to add noise into a standard distribution without increasing its variance?
Suppose I have a standard distribution dataset X with a mean 0 and std 1.
Now I want to create slight variations of this data by injecting some noise.
I could make ...
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What is difference between the joint probability distribution and the sum/convolution, of 2 dists? [duplicate]
Google is coming up a bit short when I searched for "joint vs sum random variables".
Perhaps someone can provide an authoritative answer to compare and contrast the sum/convolution of 2 ...
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Decomposing the prediction of a sum of Gaussian Processes into predictions from each Gaussian Process
Suppose the functions $f_1\sim\mathcal{GP}(m_1,K_1)$ and $f_2\sim\mathcal{GP}(m_2,K_2)$ are drawn from independent Gaussian Processes, and let
$$f=f_1+f_2.$$
Then
$$f\sim\mathcal{GP}(m,K)$$
where $m=...
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Average of random variables from two Poisson distributions?
I'm lost with a very simple question of finding the average of random variables from two Poisson distributions. I know that if $X\backsim Pois(L1)$ and $Y\backsim Pois(L2)$, then $X+Y\backsim Pois(L1+...
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Data wrangling in R with dplyr: How do I consolidate rows? United States Census data [closed]
I am analysing population projection data from the United States census and I need to present population estimates by race/ethnicity for each year from 2020 to 2029. The US census separates Asian-...
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Convergence of an infinite sum of weighted independent and identically distributed random variable
Let $z_i$ be $i.i.d$ random variable with $E(z_i)=0$ and $E(Z_i^2)=1$ with a symmetric distribution. Further, $|\beta|<1$.
Now consider $\sum\limits_{i=1}^{\infty} \beta^i (z_i+|z_i|)$. I want to ...
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How can I estimate the sum of coefficients
I am trying to estimate the cumulative effect. When I have an ols regression with many dummies as explanatory variables, can I sum the coefficients to find the cumulative effect?
If yes, how do I find ...
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Sum of dependent multivariate gaussians
Note: I have already seen this Wikipedia article, and similar questions on this website: 1.
Given two dependent multivariate Gaussian random variables, is the sum also a multivariate Gaussian?
$X \sim ...
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