# Questions tagged [summations]

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### Operator ranking of sum and plus

In the book I am reading on page 308 I find the following formula: My question is which operator has the higher rank - the sum or the plus? In other words: How would I correctly set the brackets in ...
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### Summation of Two random variable

Suppose $X$ is random variable with PDF $f(X)=2(x-1)$, $1 \le x \le 2$; $Y$ is a random variable with a triangle pdf with minimum at $2$, mode at $2.5$, and maximum at $3$. Is it possible to define ...
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### Regression proof for decomposition of sums of squares [duplicate]

I got as far as distributing the summation across the Left Side so that I have: $$\sum_i y_i^2 - \sum_i 2 y_i \bar{y} + \sum_i \bar{y}^2$$ Not sure where to go from there.
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### Which is the right way to apply PCA on different sized matrices

I am working on human age classification where I have four descriptors, namely GEI, FED, UC ...
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### Probability of union of disjoint events $[X=x \cap Y= z-x]$ for $x=0,1,...,z$ equals $\sum_{x=0}^z \mathbb{P}(X=x \cap Y=z-x)$

Why can one write $$\mathbb{P}([X=x \cap Y= z-x] \bigcup ... \bigcup [X=x+z \cap Y= z]) = \sum_{x=0}^z \mathbb{P}(X=x \cap Y=z-x)$$ ?
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### Sum of random variables without central limit theorem

I know that using central limit theorem we approximate sum of random variables into Gaussian distribution. Is the any other approximation method available for finding the probability distribution ...
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### Help with proof of factorization criterion

In a proof of the factorization criterion regarding sufficient statistics I came across the following derivation: Consider the set $A_s=[(y_1,..,y_n:s(y_1,..,y_n)=s]$ Now somewhere along the only if ...
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### Distribution of sum of function of two random variables

Let $\{x_1, \ldots, x_n\}$ be a set of $n$ i.i.d. samples from a distribution $p(x)$. I would like to evaluate the distribution of the sum $$S = \sum_{1\leq i<j\leq n} f(x_i, x_j),$$ where $f$ is ...
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### Using Poisson distribution to evaluate summations

I'm interested in how to use a Poisson distribution to evaluate $\sum\limits_{x=0}^\infty \frac{(x^2-x+1)(2^x)}{x!}$ I see that this is similar to the general pmf form of $\frac{2^{x}}{x!}$. My ...
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### Variance of a Sum

I've got the following random variable for which I must find the expected value and variance: $X_h =\sum_{i=1}^{15} X_i$ Where $X_i$ is a random variable of the set $s = \{0, 1, 3\}$, corresponding to ...
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### multi stage binomial "process"

I wish to model the retransmission time of a file that divided into K blocks. I know the successful blocks of first transmission obey the binomial distribution $$X_1 \sim \text B(K,p)$$ , p is 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 ...