Linked Questions

0
votes
1answer
48 views

Substracting two normal distributions [duplicate]

I was wondering if we have two normal distributions of X,Y~N(0,1), why is then X-2Y~N(0,5)? I understand the mean of the X-2Y distribution, but why is the variance 5?
0
votes
0answers
19 views

Computing SD for function of two RV's in R gives wrong results [duplicate]

I have 2 random variables, all independant, discrete and uniform I want to compute standard deviation for Z = X - Y Here is the R code: ...
69
votes
4answers
234k views

How to 'sum' a standard deviation?

I have a monthly average for a value and a standard deviation corresponding to that average. I am now computing the annual average as the sum of monthly averages, how can I represent the standard ...
7
votes
2answers
31k views

Why is the variance of $X-Y$ equal to the sum of the variances when $X,Y$ are independent?

I have one question about this. I know that if we have $\mathrm{X}_1,\mathrm{X}_2,\ldots,\mathrm{X}_n$ independent and normally distributed random variables, then the sum $\mathrm{X}_1+\mathrm{X}_2+\...
4
votes
1answer
2k views

Partitioning explained variance to fixed effects by comparing r squared (R2) between linear mixed models

Lets say I have 2 linear mixed models. One is simply a subset of the other. The first contains terms for 2 fixed effects and a random intercept. One of the fixed effects, "x1" I know, a priori, ...
2
votes
4answers
229 views

Creating Correlations

I have three variables, A, B, and C. It seems obvious that if X = A-B and Y = C-B that there should be a correlation between X and Y. When I've done this in matlab with random numbers, this seems to ...
2
votes
2answers
589 views

Explanation for Additive Property of Variance?

I'm wondering why variance has additive property, as opposed to why this property doesn't extend to standard deviation? Additive property is defined as: Var(A+B) = Var(A) + Var(B) I imagine this as ...
3
votes
2answers
449 views

How do I relate the std deviation of the step size, to the stdev of the endpoint of a brownian motion, if the step sizes are multiplied by a function

I know that if I take take a brownian motion of, say, 30 steps of standard deviation 1, then the standard deviation of my endpoint will be sqrt(30). But what if the standard deviation of the 30 steps ...
0
votes
1answer
404 views

Variance of a sum of functions of random variable

I'm trying to prove $$ \mathrm{Var}\left(\sum\limits_{i=1}^n{g(X_i)}\right) = n(Var(g(X_1))) $$ where $X_1...X_n$ are IID variables. I have been trying to use proof for a similar question - https://...
1
vote
0answers
399 views

Sample standard deviation or population standard deviation

I'm running an A/B testing in a website and I'm capturing the number of clicks in a given area of a page. I am calculating the average of clicks per user's session and its standard deviation. The ...
0
votes
1answer
238 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 ...
1
vote
1answer
165 views

How do I calculate the error propagation of this function?

I'm using a molecular biological method which requires the following normalization $$Q = \frac{A}{\sqrt[k]{\prod_{i=1}^k B_i}}.$$ How can I find the standard deviation of $Q$, given that $A$ and $...
0
votes
1answer
169 views

Sum of variances law

I am currently trying to grasp the concept of Variance Sum Law where variance(x + y) = variance(x) + variance(y) I am not even sure if I understand it correctly ...
0
votes
1answer
89 views

What is my missing assumption is sum of variances?

In this answer, it says that in general the sum of the variances is not equal to the variance of the sum. I tried to work it out by myself, and I think I got a different result, namely that the ...
0
votes
0answers
82 views

Relationship between correlation of x vs. x+y and y vs. x+y [duplicate]

I am working with some data in which two component scores X and Y are added together to make a total score X + Y. Is there any known relationship between the correlation R for X vs. X + Y and the R ...