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3
votes
1answer
35 views

Proving a property of $(n-1)s^2$

I would appreciate your help as I climb the stats learning curve! I want to prove the following: "Let $x_1, x_2, ... , x_n$ be any numbers and let $\overline x = (x_1 + x_2 + ... + x_n)/n$ Then ...
0
votes
2answers
23 views

What is the variance of the sum of Yi's

Seems a simple enough question, and I presume that, if Yi are normally distributed, Var(Sum(Yi)) = Sum(Var(Yi)) This feels like I'm jumping to the wrong conclusion though. Any help would be ...
1
vote
1answer
29 views

Formative/composite variable as weighted additive index

I'm very new to SEM (and relatively new to stats generally). I would like to ask whether my plans generally sound reasonable before I get lost for days in the literature. The model that I try to work ...
1
vote
1answer
28 views

Characteristic function issue

As mentioned in a previous post, I've been trying to work through ALL of the problems in Jacod and Protter's Probability Essentials. The following problem has been giving me issues: Let $Z \sim ...
0
votes
1answer
13 views

Solving for a difference equation for $s_{t}$

Given $f_{t}=u_{t} - \bar{P}$ and the law of motion for $u_{t} = \rho u_{t-1} + \epsilon_{t}$, where $0<\rho<1$, $\epsilon_{t}$ is mean-zero iid and can be interpreted as a domestic price level ...
0
votes
0answers
24 views

How to represent the sum of two linear model predictions in same unit

I have built two linear regressions independently of one another, and $Y_1$ and $Y_2$ are in the same units. I am interested in using the sum of $\widehat{Y}_1$ + $\widehat{Y}_2$ (the predictions) to ...
3
votes
1answer
46 views

Prove that sum of uniform distribution (-1,1) is also uniform (-n,n)? [duplicate]

If $d_i \in U(-1,1)$ (uniform distribution between -1 and 1 - not sure what the canonical notation is for this), then it seems intuitive that $\sum_{i=1}^n d_i \in U(-n,n)$ and thus ...
0
votes
1answer
49 views

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 ...
0
votes
0answers
18 views

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 $$\mathbb{P}([X=x \cap Y= z-x] \bigcup ... \bigcup [X=x+z \cap Y= z]) = \sum_{x=0}^z \mathbb{P}(X=x \cap Y=z-x)$$ ?
0
votes
0answers
10 views

Sum of ordinal items, treated as non-parametric?

I have a survey which seeks to quantify the amount of experience with performing arts. Each item as the person questions like "estimate the numbers of experience you have had playing an instrument ...
5
votes
2answers
81 views

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 ...
0
votes
1answer
42 views

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 ...
0
votes
0answers
41 views

Quantile aggregation for a sum of dependent variables

I am currently working with a sum of dependent variables following complex laws. For these laws I have a vector of means, $\mu$ and a linear correlation matrix $\Sigma = \rho_{i,j})_{i=1..n,j=1..n}$. ...
4
votes
2answers
109 views

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 ...
4
votes
1answer
104 views

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 ...
0
votes
1answer
66 views

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 ...
0
votes
1answer
89 views

Measuring share contribution of each var/cov term to the standard deviation of a sum of variables

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 ...
0
votes
1answer
2k 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 ...
7
votes
1answer
243 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 ...
2
votes
0answers
191 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.
5
votes
1answer
49 views

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 ...
2
votes
0answers
27 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 ...
0
votes
0answers
119 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 ...
1
vote
2answers
110 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?
4
votes
1answer
107 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 ...
0
votes
0answers
84 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, ...
2
votes
0answers
388 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 ...
1
vote
0answers
73 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 ...
14
votes
3answers
3k 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 ...
1
vote
0answers
53 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 ...
1
vote
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
vote
1answer
58 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
votes
1answer
154 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 ...
0
votes
1answer
243 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 ...
0
votes
1answer
2k 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
votes
1answer
84 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
votes
1answer
686 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
vote
1answer
153 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 ...
0
votes
0answers
95 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} ...