# 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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Say, for a simple example, I have a random variable $X = \alpha_1 X_1 + \alpha_2 X_2$, where $X_i$ are random variables and $\alpha_i$ are weights. I then calculate the standard deviation of $X$ as $\... 1answer 18k views ### In SPSS, should I calculate the mean score or the total sum score? Are there any differences between mean scores and total sum scores? I know how to calculate both, I just don't know if there is one of them that is preferable? Also, the scores will be used for t-... 1answer 4k views ### What does it mean if the median or average of sums is greater than sum of those of addends? I'm analyzing the distribution of network latency. The median upload time (U) is 0.5s. The median download (D) time is 2s. However, the median total time (for each data point, T = U + D) is 4s. What ... 1answer 2k views ### Expectation of cube of summation of independent random variables Where would I begin on this problem? I know I begin with pulling$c^3$. Where would I go from there? And I know that$\mathbb{E}[X] = x_1p_1 + .... x_n p_n\$ I'm stuck on the rest, however.
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 ...