Questions tagged [sum]

The sum of two or more random variables.

65 questions
35 views

Inferring random variables from their sum

Suppose I have a large set of receipts that list the items I bought, but only list the total cost. One day I might have bought Milk, Butter, and Eggs. A different day I might have bought Bread, Milk,...
51 views

Deconvolution of the sum of three gaussian distributions

Consider the sum of three normal random variables: $R_{i,j}=A_{i}+B_{j}+C_{i,j}\,$ where $A_{i}∼N(μ_{A},σ_{A})$ , $B_{j}∼N(μ_{B},σ_{B})$ and $C_{i,j}∼N(μ_{C},σ_{C})$ . Assuming $A$, $B$ ...
40 views

Force sum of random varables to equal to 1 [duplicate]

Suppose I have 3 random variables, $X1, X2,X3$. Define $Z$ as: $Z=X1+X2+X3$ I want to force $Z$ to equal 1 for every "realization" of $X1,X2,X3$ ($X_i \sim Beta(a_i,b_i))$. As an example, let $X_i$ ...
37 views

Understanding the infinite sum of random variables

I am doing a course on time series analysis, and am struggling with this definition: We call a weakly stationary process $\{X_t\}$ invertible with respect to a white noise $\{\epsilon_t\}$ if ...
51 views

How to check these sequences generated by i.i.d random variables are martingales?

Let $\{Y_n\}_{n\geq 1}$ be a sequence of independent, identically distributed random variables. $P(Y_i=1)=P(Y_i=-1)=\frac12$ Set $S_0=0$ and $S_n=Y_1+...+Y_n$ if $n\geq 1$ I want to check if the ...
67 views

Is the sum of trends of two time series the trend of the sum of the time series?

Let's say I have two time-series, A and B. I build time-series C as C=A+B. I estimate the trend of A, let's say I get +0.5 (Theil-Sen). I estimate the trend of B, let's say I get -0.4 (Theil-Sen). ...
58 views

Mean of root-sum-square of

Suppose that I have several normally-distributed random variables xi, each with its own different variance. All x's are zero-mean and independent. If y is the root-sum-square of the xi's, how do I ...
13 views

Confusion about the derivation of the TD-Learning update rule

I am currently trying to understand the paper "Learning to Predict by the Methods of Temporal Differences" by Sutton. I am stuck with the following step: (From "Learning to Predict by the Methods of ...
17 views

468 views

Sum of predicted values to the power of 10 [closed]

When I take predicted values from a linear model to the power of 10, their sum is always a lot bigger than the original. Is it even allowed to sum, and does anybody have a reference for how this ...
207 views

Linear combination of non central chi-squared random variables

I want to analyze the distribution of $$X = \sum_i X_i^2$$ where independent $X_i \sim \mathcal{N}(\mu_i, \sigma_i^2)$. If $\mu_i=0$, I can derive the distribution by passing Gamma distribution like ...
183 views

615 views

Distribution of the sample mean of Poisson random variables

Suppose that you have data x which is modeled as a realization of a Poisson random variable X with expected value $\lambda$>0. I know that the sum of Poisson random variables is also Poisson ...
133 views

a single estimate and the population mean

There is a physical parameter $Z$ defined as $Z=\frac{X}{X+Y}$, where $X=\sum_{i=1}^{N} x_i$ and $Y=\sum_{i=1}^{N} y_i$. I want to find an interval that brackets the population mean $\mu_Z$ for a ...
83 views