Questions tagged [sum]
The sum of two or more random variables.
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Concentration of sum of geometric random variables taken to a power
I am interested in techniques for showing the concentration of sum of $n$ iid geometric random variables $X_1, X_2, \cdots, X_n$ (number of trials until success), say with success probability $p = 1/2$...
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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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Conditional expectation, conditional on sum of weighted average of two iid RVs
I have an arbitrary distribution $F$, and two variables $z, x \sim F$.
I only observe the weighted average $y = \alpha z + (1 - \alpha) x$. Conditional on $y$, what is the expected value of $z$?
I ...
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Mean number of throws to exceed a threshold [duplicate]
Say that you have a die with n faces, and you need to throw the die until the sum of your results exceeds a given threshold.
What is the average number of throws needed?
I think that to compute that ...
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Sum of estimated costs for uncertain events
I have a number of possible events $e$ with a probability $p_e$ of the event occuring and a cost estimate should the event occur (if it doesn't occur the cost is 0). The probability for each event is ...
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Summation notation
I am reading a statistics book which says:
" If $ X \sim N ( \mu, \sigma^2)$, it is verified that:
$ \sum_{i=1}^{n}X \sim N ( n\mu, n\sigma^2) $
My doubt is if it should have been written as $ ...
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What is the expectation of $\left\langle (n \bar{y})^4 \right\rangle$, if $y_i \sim \mathcal{N}(\mu,\sigma^2)$?
Let $y_i \sim \mathcal{N}(\mu,\sigma^2), \; i = 1,\ldots,n$ and $\bar{y} = \frac{1}{n} \sum_{i=1}^n y_i$, such that $n \bar{y} = y_1 + \ldots + y_n$.
Then, we want to know what the expectation of $(n \...
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Fast Evaluation of a Double Sum
Let
$q$ be a probability distribution on $\mathcal{X}$,
$w$ be a nonnegative function from $\mathcal{X}$ to $\mathbf{R}$ which is bounded away from $0$ and $\infty$, and
$s$ be a bounded function ...
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How can we decompose $\text{Var}[\sum_{i=1}^n\sum_{j=1}^m f(A_i,B_j)]$?
Formulas for decomposing the variance of a summation of random variables can be found on Wikipedia but what is the variance of a double summation of a function of random variables? That is, are there ...
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Is there a way to prove $\mathbf{\hat{Y}}^T\mathbf{e}=\mathbf{0}$ without resorting to summations?
I would like to show that $\mathbf{\hat{Y}}^T\mathbf{e}=\mathbf{0}$. I can solve this by saying that it is equivalent to showing $\sum e_i\hat{y}_i=0$. However, I'm wondering if there is a way to ...
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Probability of compound Poisson process
Let $X$ be a compound Poisson process with rate $\lambda$ and increments $Y_i = \pm 1$ with probability $\frac{1}{2}$. Find $P(X(t) = 0)$.
I tried conditioning on $N(t)$:
$$
P(X(t) = 0) = P(\sum\...
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Sum of Bimodal Distributions? [closed]
If I'm trying to estimate a the sum of a bunch of random variables, where each random variable is a bimodal distribution, how would i go about thinking or modeling what that looks like?
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Z-Score for Sum of Proportions?
First, please bear with me. I am not very savvy with statistics, so I may be mixing up terms or using things improperly. Second, I am dealing with statistics related to baseball, so let me explain ...
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Sum of IID normal variables with index following Poisson distribution
$X_1, X_2,\ldots$ are a sequence of independent normal random variables with mean 1 and variance 1.
Calculate the variance of $X_1+X_2+X_3+\ldots+X_{N+1}$ where $N$ follows Poisson distribution with ...
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What statistical test can compare the sum instead of the mean?
I'm confused about if t-test can only test means (sum / sample size), or if it can test sums as well (not normalizing for sample size).
Below is a passage from a trusted book.
Note that even though ...
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