Questions tagged [sum]
The sum of two or more random variables.
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Generic sum of Gamma random variables
I have read that the sum of Gamma random variables with the same scale parameter is another Gamma random variable. I've also seen the paper by Moschopoulos describing a method for the summation of a ...
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The sum of independent lognormal random variables appears lognormal?
I'm trying to understand why the sum of two (or more) lognormal random variables approaches a lognormal distribution as you increase the number of observations. I've looked online and not found any ...
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Probability that sum of binary variables is even
Let $S_i \in \{0,1\}$, $i=1,\dots,N$ be $N$ independent random binary variables, each taking the value 1 with probability $0 \le p_i \le 1$ (and the value 0 with probability $1-p_i$).
I am interested ...
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What does it mean if the median or average of sums is greater than sum of those of addends?
I'm analyzing the distribution of network latency. The median upload time (U) is 0.5s. The median download (D) time is 2s. However, the median total time (for each data point, T = U + D) is 4s.
What ...
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Central Limit Theorem for square roots of sums of i.i.d. random variables
Intrigued by a question at math.stackexchange, and investigating it empirically, I am wondering about the following statement on the square-root of sums of i.i.d. random variables.
Suppose $X_1, X_2, ...
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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 interpret sum of two random variables that cross domains?
suppose we have two discrete random variables:
$X: \{$6 sided dice rolls$\}$ $\rightarrow \{1..6\}$ (following uniform distribution)
$Y: \{$coin flips$\}$ $\rightarrow \{0,1\}$ (following uniform ...
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Finding the distribution of sum of Lognormal Random Variables
I am trying to find the distribution of sum of 2 lognormal random variables. I referred the literature available on Cross validated, Stack overflow and few papers before posting this.
I used ...
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3
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Is the sum of two singular covariance matrices also singular?
I have two sample covariance matrices, computed from $n$ samples, less than $p$ variables: they are singular then.
I know that the sum of two covariance matrices is also a covariance matrix.
My ...
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PDF of sum of truncated exponential distribution
Let $x_i$ represent samples from a Truncated Exponential distribution between $0$ and $1$, with rate parameter $\lambda$.
Defining
$\tilde x = \dfrac{\sum_{i=1}^{n}x_i}{n}$
What is the PDF of $\...
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Sum of sample given a priori knowledge of its maximum
Given a sample of discrete random variables $X_1, X_2, \ldots, X_n \sim F$, I am looking to calculate the distribution given by the probability mass function:
$$P\left(\sum_{i=1}^n X_i = x~\middle|~\...
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If $20 $ random numbers are selected independently from the interval $(0,1) $ probability that the sum of these numbers is at least $8$? [closed]
If $20 $ random numbers are selected independently from the interval
$(0,1) $ what is the probability that the sum of these numbers is
at least $8$?
I tried to take this question https://math....
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Sum of forecasts
I have a question regarding forecast. I'm building an inventory model around warehouses, where all warehouses have multiple customers/countries assigned. I have data on sales for all countries ...
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Front-Door Adjustment formula: confusing notation
Pearl et al. "Causal Inference in Statistics: A Primer" (2016) p. 69 Theorem 3.4.1 provides the Front-Door Adjustment formula:
$$
P(y | \text{do}(X = x)) = \sum_z P(z | x) \sum_{x'} P(y|x', z)P(x').
$$...
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Finite sum of beta prime iid random variables
The beta prime distribution is infinitely divisible, as proved in Steutel and van Harn, 2003 (Appendix B). Sadly, in this book, there is no expression of the parameters of the distribution of $n$ ...
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