# Questions tagged [sum]

The sum of two or more random variables.

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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 &...
1 vote
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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. ...
520 views

### 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&...
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 ...
157 views

### 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 \begin{equation} f_Y(y) = \sum_{i=1}^{2}\pi_i f(y| \lambda_i) \end{equation} where $\pi$ stands for ...
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