# Questions tagged [sum]

The sum of two or more random variables.

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17 views

### Proportion of the sums or average proportion of the parts?

Here’s a curiosity that come up during a work discussion. While this example uses financial data, it has a statistical question at its heart. Consider the following table with a budget and actual ...
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### I need to find the Z-score of a population to use as a cutoff point in order to reduce the value sum of numbers to a new sum

This may be tough to describe, but I'll give it a shot. I am setting up an analysis that produces a large set of numbers. Let's call this Analysis 1 (A1). If I run A1 and return 60 numbers with a ...
208 views

### Is there a statistical distribution whose values are bounded $[-1,1]$ and sum to 1?

The Dirichlet distribution contains values that are bounded $[0,1]\in \mathbb{R}$ and sum to $1$. Is there a parametric distribution or similar method whose values do the same but reach as low as $-1$?...
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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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### How to calculate this dependent probability (marbles without replacement)?

I present the question in two steps: First: Let there be 100 bags. A person puts 5 marbles into 5 separate, randomly selected, bags. You are now to collect the contents of the bags, one by one. If you ...
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### Expectation of sum of absolute values for correlated normal random variables

Let $x_1, x_2, \dots, x_{N}$ i.i.d. random variables $\sim \mathcal{N}\left(0,\sigma^2_x\right)$. Further, let $z\sim \mathcal{N}\left(0,\sigma^2_z\right)$, $z$ is independent from all $x_i$. We build ...
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### Difference of two independent lognormal random variables by Fourier transform methods?

Is it possible to calculate the difference $X_1-X_2$ of two independent lognormal variables $X_1$ and $X_2$ where $\log(X_1)\sim N(\mu_1,\sigma_1)$ and $\log(X_2)\sim N(\mu_2,\sigma_2)$? Could I ...
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### Is an uneven item number over different facets of a factor a problem?

I have developed a new questionnaire for specifically 1 factor with 4 facets. At first, all 4 facets have the same number of items. I create sum variables and dataframes from them to analyze the ...
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### How to derive this inverse standard deviation error bound for binomial random variable? [duplicate]

Is this error bound suggesting the normal approximation is good for binomial random variables? How was it derived? Why is the reciprocal standard deviation in the error bound?
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### X~Unif(0, 1) ; X1 + X2 + … X6 = 1 ; Y = sum(X1…X6) ; VAR(Y) =?

Let $X_i$ ~ Unif(0, 1) s.t. $X_1 + X_2 + ... + X_6 = 1$ Let $Y = X_1 + … X_6$ What is $Var(Y)$? (Also the case when it's $X_n$) Purpose for the curious: I'm trying to rank confidence for softmax ...
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### What does “The mean of the sum of N independent variables with the same distribution is N times the mean of a single variable” mean?

I have been reading a book about statistics for physicists and there was this line given: "The mean of the sum of N independent variables with the same distribution is N times the mean of a single ...
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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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### Perform signed rank test where there are duplicates in data?

How do you perform a rank test when there are duplicates in the data? that is, we have a dataset with numbers $1,1,1,1,3,3,3,3,4,4,4,4.$ and another dataset also with duplicates.... Is the sum of ...
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### How do I find the conditional distribution of a normal r. v. z, given that I know the sum of z and another normal r. v. x is greater than some value?

Suppose I have two independent normal random variables, $X$ and $Z$ with $\mu_x$, $\sigma^2_x$ and $\mu_z$, $\sigma^2_z$. Suppose I also know that $x+z\geq y$. How do I find the conditional ...
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### Why is $\sum{(x_i-\overline{x})^2}$ = $\sum{(x_i-\overline{x})x_i}$ true? [duplicate]

I have seen this equality many times in books but I never found an explanatory derivation.
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### Infering noise conributions on the sum of normal RV's

Suppose multiple factors affect the noise in a measurement, e.g. a manufacturer may have some variance between production runs ($\sigma_1^2$), and some variance between products within the same ...
33 views

### 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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### How can I prove these propositions of infinite sum of random variables?

$x_1, x_2, x_3, ..., x_i, ...$ ~ $uniform(0, 1)$ The actual random variable is the following. $P_i = (1-x_1)(1-x_2)...(1-x_{i-1})x_i$ And the goal is proving these... $\sum_{i=1}^{n}P_i \leq 1$ If ...
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### Is the error term a sum of r.v.?

`If in a econometric model I have: $y = \beta x + u$ where u is the error term, we have: $u = y - \beta x$ Supposing that $\beta=1$, $y\sim N(0,1)$, $x \sim N(0,1)$ and $x$, $y$ are independent. ...
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### Comparing sum of values of two groups

I have a question about how to make a comparison between the aggregate values of two experimental groups. Say that in an experiment with a control group and a treatment I collect the number of times ...
162 views

### Probability of sum of sequences of integers

Let K be a positive integer.Suppose that the integers 1,2,3,...,3k+1are written down in random order.What is the probability that at no time during this process, the sum of the integers that have been ...
199 views

### How could “sum of exponential distribution is 1” be proven?

$$f(x; \lambda) = \begin{cases} \lambda e^{-\lambda x} \quad \text { for } x \geq 0 \\ 0 \quad \quad \quad \text { for }x < 0\end{cases}$$ How can I prove that the sum of probabilities under ...
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### Summation of squared x_i if summation of x_i is 1

How to prove "If $\sum_{i=1}^n x_i=1$, then $\sum_{i=1}^n x_i^2>1/n$"? I'm thinking about $Var(x_i)=E(x_i^2)-[E(x_i)]^2=\frac{1}{n}\sum_{i=1}^n x_i^2-1/n^2\ge0$. Is that correct?
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### Covariance of random variables whose sum is less than a constant

Suppose that we have integer random variables $X>0$ and $Y>0$ and constant number $a$. We have: $X+Y < a$. Can we say that the covariance of these random variables is less than or equal to ...
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### Sum of 2 Normally Distributed Random Variables With a Correlation

I've been given a problem where I have $$X \sim \mathcal{N}(\mu = 2, \sigma^2 = 9)$$ $$Y \sim \mathcal{N}(\mu = 3, \sigma^2 = 4)$$ Their correlation is $\rho_{XY} = 0.6$. First I am asked for ...
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### Summing up double series under constraints on the indexes

I have the following double sum: $$\sum_{t=0}^\infty \sum_{\ell=0}^r \psi(t,\ell,r),$$ only for even values of $t+\ell$ or $t+\ell=0$. First, I thought, since $\ell$ depends on $r$, and $r$ can ...
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### Generate identically distributed dependent normal random numbers with prespecified sum

How do I generate $n$ identically distributed but not independent normal random numbers such that their sum falls within a prespecified interval $[a,b]$ with probability $p$? (This question is ...
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### Question regarding the distribution of sum of random variables

Let $X_1, ... X_n$ be i.i.d random variables that have an exponential distribution with parameter $\theta$. So we know that $\sum X_n \sim \Gamma(n, \theta)$. This makes sense by working backward. ...
If $X,Y$ are $\geq 0$ random variables, how to demonstrate that: $$2*Stdev(X) \leq Stdev(X+Y)+ Stdev(X-Y)$$ $Stdev$ represents the usual standard deviation.
I don't know if the title is accurate, but I have this problem: I have iid RVs $Y_k$ that has a value from {0,1,...,9} with equal probability. I need to show that $$X_n = \sum_{k=1}^{n}Y_k10^{-k}$$ ...