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4
votes
1answer
77 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
85 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
40 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
25 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
200 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 ...
6
votes
1answer
63 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
60 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
42 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
20 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
65 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
99 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
98 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
243 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
56 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 ...
12
votes
2answers
1k 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
47 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
55 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
143 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
224 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
1k 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
77 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
556 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
138 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
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} ...