Questions tagged [sum]
The sum of two or more random variables.
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Summation of a product
I need to calculate the following expression:
$$\sum_{k=1}^N a_k b_k$$
${a_k}$ and $b_k$ are real positive numbers. N and k are integers.
I know the average values of $a_k$ , defined as $\overline {...
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variance of summation/compound variable?
here is my situation. I am weighting a packet of material that has 10 individual units in it. In the end of the day I would like to know the average weight and variance of the individual units but the ...
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Generic sum of Gamma random variables
I have read that the sum of Gamma random variables with the same scale parameter is another Gamma random variable. I've also seen the paper by Moschopoulos describing a method for the summation of a ...
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Random variables for which the distribution of the sum of the RV with a Gaussian RV is known
For a counter example, I am searching for random variables $Y$ such that for a independent normal random variable $X$ the distribution of $Z=Y+X$ is known parametrically. Ideally, the Shannon entropy ...
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Why is this MGF identity true?
If $X_i \overset{i.i.d.}\sim N(\mu, \sigma^2) $, we know that: $\bar{X} \sim N(\mu, \sigma^2 /n)$.
But why does:
$$\exp\left({\sigma^{2}\over 2}\sum_{i=1}^{n}(t_{i}-\bar{t})^{2}\right)= M_{X_{1}-\bar{...
user19860
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What can we conclude about the distribution of the sum of two random variables?
If we know, for independent random variables $X$ and $Y$,
$P(X>x)\leq0.05$, and $P(Y>y)\leq0.05$, can we say anything about $P(X+Y>x+y)$? Can we be certain that it is less than $0.05$? Under ...
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How to rewrite a sum of probabilities formula as multiplications?
I have an equation like that:
$p(r|s)= \frac{p(s,r)}{p(s)}=\frac{ \sum_{w,c} p(c,s,r,w)}{\sum_{w,c,r} p(c,s,r,w)} $
I am new to probability and I want to learn that how can I write sum formula as ...
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Sum(XY) in terms of Xbar and Ybar [closed]
If $x$ and $y$ are two series, is there any relation between $\sum{(x,y)}$ that can be expressed in terms of mean of these two. Specifically, I want to know if any sort of relation exists between $\...
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Getting past independence assumptions in modeling the sum of random variables (application in education)
I'm trying to model a student's semester GPA $G$ as a random variable.
Semester GPA is a weighted (based on credit hours) sum of a student's grade points (e.g. 0=F,1=D,2=C,3=B,4=A).
We can consider ...
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Deriving OLS estimates using method of moments
I've worked the slope all the way down to $\sum [x_i(y_i - \bar{y})] = \hat\beta_1 \sum[x_i(x_i - \bar{x})]$
But I can not figure out how to show the steps for:
$\sum[x_i(y_i - \bar{y})] = \sum(x_i -...
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Estimate variance of sub-sets from overall variance
I am looking for a way to estimate the variance of a summed sub-set based on the variance of those sums.
Si = sum( Ai )
S = { S0...Sn }
V = variance( S )
That is,...
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Understanding summations in COV formula for time series
I am looking through Time Series Analysis: With Applications in R (my first exposure to time series) and refreshing summations.
I.
When given the following rule:
COV[$\sum_{i=1}^{m} c_{i}Y_{t_{i}},\...
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