# Questions tagged [sum]

The sum of two or more random variables.

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### Confidence interval for the sum of 2 binomially distributed variables

$P_1$ and $P_2$ are uncorrelated, binomially distributed variables with success probabilities $p_1 \neq p_2$. Say I measure: $k_1 = 9$ successes out of $n_1 = 10$ trials for $P_1$ and $k_2 = 1000$ ...
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### PDF of difference of uniform distributions [duplicate]

Main questions are in bold but feel free to correct me if I'm wrong somewhere else. As far as possible, I need both intuition and formal explanation. Let $X \sim Uniform(a,b)$ and $Y \sim Uniform(c,d)$...
1 vote
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### how to statistically test two sums of 1s [closed]

I have the following vectors: vec_1=c(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1) vec_2=c(1,1,1,1,1,1,1,1,1) from which I compute the corresponding sums: ...
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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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### Conditional probabilities of the parameters

I have the following function $$x(k) = \sum_{m}^{M} e^{i(U_m k + \beta_m)}$$ Where $$i = \sqrt{-1}$$ The $U_m$ values come from a normal distribution and the $\beta_m$ values come from a uniform ...
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### Time series benchmarking/reconciliation and revisions - are there methods that minimise revisions?

I am using the tempdisagg R package for benchmarking quarterly time series to annual time series from different (more trusted) sources (by temporally disaggragating the annual data using the quarterly ...
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### Does $p=0 \implies \sum_{i=1}^{p} \phi_i L^i = 0$?

Let us take this $\operatorname{AR}(p)$ equation $$\left(1 - \sum_{i=1}^{p} \phi_i L^i \right)X_t = \mu + \epsilon_t$$ as an example. When $p=0$ I read this to mean \begin{align*} \mu + \epsilon_t &...
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### Is there a clear interpretation of Corr(X, X+Y) in research?

Consider a case of $Corr(X,Z)$, often found to be high; where later, it was found that it holds exactly $Z = X + Y$. In effect, the previously found correlations were equal to $Corr(X, X+Y)$. How can ...
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### If X=Y+Z, Is it ever useful to regress X on Y?

If we have X and Y that are mathematically dependent: X = Y + Z, is it 'forbidden' to use Y as a predictor to X in linear regression? I'm trying to find a concise explanation for why it is, or isn't. ...
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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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### Prove $P(X_1+X_2> 2C) \leq P(X_1>C)$ if $X_1,X_2$ are identical, but dependent?

If $X_1,X_2$ are dependent but identically distributed, it seems obvious that $P(X_1+X_2\geq2C) \leq P(X_1\geq C)=P(X_2\geq C)$. At least if we additionally assume that the joint distribution is ...
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### Statistical Data Analysis using "Sum" Function

Most commonly when I hear descriptive data analysis using statistics these following functions are often inclded: Mean Standard Deviation Variance Range Mode Median etc. Is the function "Sum&...
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1 vote
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### Calculating the probability of the total duration of N sequential events with different cdfs describing their duration

Be patient, I am not very skilled with cdf. I seem to have a seemingly simple problem for which I either can't seem to find material about or simply lack the vocabulary for. Given are N sequential ...
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### Distribution of sum of $n$ random variables with mixture of two exponential distributions

Suppose that the random variable $Y$ follows a mixture of two exponential distributions, that is $$f_Y(y) = \sum_{i=1}^{2}\pi_i f(y| \lambda_i)$$ where $\pi$ stands for ...
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### sumscores instead of factorscores or SEM

Suppose I would like to use sumscores after running a confirmatory factor analysis (CFA) with two latent factors. The items for each factor are then summed and in subsequent analyses these sums are ...
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### Sum of Discrete Uniforms, but each value can be picked no more than N times?

Suppose there are i.i.d. variables $X_{1,..n}$ with discrete uniform distribution with the support $[1, n]$. What would be the distribution of such a sum if we introduce the condition that each value ...
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### For k independent variables, if each one is independent of $Y_1$,...,$Y_p$, how to formally prove their sum is also independent of each $Y_p$?

SUppose I have $X_1,...,X_k$ independent of each other. I also have $Y_1,...,Y_p$ is independent of each other. If each one in $X_1$,...,$X_k$ is independent of each one in $Y_1$,...,$Y_p$, how to ...
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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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### Consistency when we want to find the distribution of sum of random variables following each one a distribution

I want to clarify a point that disturbs me among different cases. I am interested in formulate correctly in a general case when we know the distribution of different random variables and we want to ...
Suppose I have 7 variables $y_i$ sampled from $Gamm(a,1)$, with $a>0$. Now, I define $$x_1 = y_1+y_2+y_3+y_4,$$ $$x_2 = y_1+y_2+y_5+y_6,$$ $$x_3 = y_1+y_3+y_5+y_7$$ What is the distribution of $x_1$...
I'm having trouble finding a way to do this calculation and checking if I'm correct: Let $X_1 \sim Exp(2)$ and $X_2 \sim Exp(2)$ be independent random variables $\left(f_X(x) = 2e^{-2x}\right)$, ...