Questions tagged [sum]
The sum of two or more random variables.
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Square roots of sums absolute values of i.i.d. random variables with zero mean
In an earlier question, I asked about the limiting distribution of the square root of the absolute value of the sum of $n$ i.i.d. random variables each with finite non-zero mean $\mu$ and variance $\...
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Measuring share contribution of each var/cov term to the standard deviation of a sum of variables
Say, for a simple example, I have a random variable $X = \alpha_1 X_1 + \alpha_2 X_2$, where $X_i$ are random variables and $\alpha_i$ are weights. I then calculate the standard deviation of $X$ as $\...
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Any known approximations of summing quantiles from joint (bernoulli / lognormal) distributions
This is my first post to this site!
For an insurance-like scenario, I have several independent risks which I want to sum together and find a 95% percentile. Currently I do this by Monte Carlo but I ...
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When (if ever) is the sum of two dependent geometric RVs negative binominal?
Imagine you have two random variables $X $ and $Y$, you know
$$
X \sim \text{Geometric}(p) \\
X + Y \sim \text{Negative Binomial}(2, p)
$$
I am interested in what if anything can be said about the ...
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Summation of combinations up to $r-1$ terms
I am trying to come up with a simplified expression for $$\sum_{k=r}^{n}\binom{n}{k}$$
Choosing $x=y=1$ in Binomial theorem, I have $$2^n = \sum_{k=0}^{n}\binom{n}{k}$$ $$2^n = \sum_{k=0}^{r-1}\binom{...
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Estimating the distribution of a sum of two random variables if the family of one of the variables is known
Assume I have a random variable $Y=X_1+X_2$. I want to estimate the distribution $f$ of $Y$ given a sample $y_1,\ldots,y_N$. If this was all that is known about $Y$ the best way would probably be to ...
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Decomposing the prediction of a sum of Gaussian Processes into predictions from each Gaussian Process
Suppose the functions $f_1\sim\mathcal{GP}(m_1,K_1)$ and $f_2\sim\mathcal{GP}(m_2,K_2)$ are drawn from independent Gaussian Processes, and let
$$f=f_1+f_2.$$
Then
$$f\sim\mathcal{GP}(m,K)$$
where $m=...
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When is $\sum Z_i \sim \sqrt{n} Z_i$?
If $X_i$ are independently and identically distributed $N(0,\sigma^2)$ then $Y=\sum X_i \sim N(0,n\sigma^2)$, i.e. $\sum X_i \sim \sqrt{n}X_i$. That raises two questions:
Is a zero-mean normal ...
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Numerical evaluation of infinite sums
I am working with Skellam random variables and I would like to evaluate the CDF of the absolute value of a Skellam random variable in which both Poisson random variables have the same rate, $\lambda_1 ...
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Limiting distribution of infinite sparse sum
Let $N$ be a positive integer.
I consider $N$ random variables $X_1^{(N)}, X_2^{(N)}, \dots, X_N^{(N)}$, all independent and identically distributed, each taking values $\pm 1$ with probabilities $p/(...
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Summation of Series involving Exponential terms
I'm currently working on a problem, which involves Poisson-Binomial Distribution. https://en.wikipedia.org/wiki/Poisson_binomial_distribution
. The Mean of PBD is given by $M=\sum_{i=1}^{n}p_i$ ....
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Propagation possion errors on scaled count bins
I have a count-channel histogram, where the counts have a standard Poisson uncertainty - if bin $i$ has $C_i$ counts then the uncertainty is $\sqrt{C_i}$.
Now if I were to sum all the bins my job ...
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How to calculate a new mean from different means for my Systematic Review and how to calculate a new SD?
I am currently doing a systematic review on distal radius fractures. I want to give a mean age and sd in my systematic review. Therefor I need to calculate the mean from all the different means of the ...
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Standard deviation of number of terms in a sum
If some random variables are drawn from a normal distribution N(m, s) with m > 0 until the sum of the draws exceeds some ...
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Summation of a product
I need to calculate the following expression:
$$\sum_{k=1}^N a_k b_k$$
${a_k}$ and $b_k$ are real positive numbers. N and k are integers.
I know the average values of $a_k$ , defined as $\overline {...
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