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11 views

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 ...
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0answers
12 views

Calculate variance of subpopulation given variance of overall population and its complement

I'd like to be able to calculate the sample variance for a subpopulation [B] given the sample mean and variance for its complement [A] and the overall population [A+B]. I have the sample mean and ...
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0answers
11 views

how can i calculate square sum of all the products of the summation? [migrated]

Rule.‚ÄČ The square of a sum is equal to the sum of the squares of all the summands plus the sum of all the double products of the summands in twos: But I do not know how to calculate the square of ...
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2answers
91 views

Sum of combination

My problem is: Evaluate: $$\sum_{i=0}^n i{n \choose i}$$ I only know that $$\sum_{i=0}^n{n \choose i} = 2^n$$ not so sure when an "i" is added. What is the step of this evaluation?
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0answers
11 views

Adding the variances of spatially correlated data

I have a geographical grid, for every cell in that grid I know that the variable I am looking at is normally distributed and I have its mean and variance. Now, imagine I am looking at an individual ...
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1answer
87 views

Sum of products in an expected value

A box contains $n$ balls numbered from 1 to $n$. Suppose you take a ball at a time, putting it back on the box, until you pick a ball twice. How many balls are you expected to take from the box? Let ...
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0answers
72 views

Appropriate statistical test

I know little about statistics. Help me, StackExchange! The software I'm working on does what I believe may be a dubious test. Suppose we measure three values (not real data): $$A) Mean = 10.5, ...
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0answers
123 views

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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0answers
48 views

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 ...
11
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1answer
491 views

General sum of Gamma distributions

I have read that the sum of gamma distributions with the same scale parameter is another gamma distribution. I've also seen the paper by Moschopoulos describing a method for the summation of a general ...
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0answers
42 views

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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0answers
35 views

How to find the optimum ordering of a set for a nonlinear equation in decent time

Assuming I have an unordered set of tuples of the form: $(a, b)$ How can I order the set so as to optimize the following equation: $\sum_{i=1}^n\sum_{j=1}^{i-1}(a_i*b_i)(1-b_j)$ For small ...
1
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1answer
54 views

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)= ...
4
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1answer
139 views

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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1answer
209 views

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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1answer
904 views

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 ...
2
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1answer
74 views

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 ...
2
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1answer
432 views

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 ...
1
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1answer
98 views

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 ...
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0answers
94 views

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} ...