Mean of Sum of IID Random Variables

ObliviousSage
Messages
36
Reaction score
0
If X is some RV, and Y is a sum of n independent Xis (i.e. n independent identically distributed random variables with distribution X), is the mean of Y just the sum of the means of the n Xs?

That is, if Y=X1+X2+...+Xn, is E[Y]=nE[X]?

I know that for one-to-one order-preserving functions, if Y=h(X) then E[Y]=E[h(X)] with a single variable X, but I'm not sure if it works with multiple Xs, even with something as simple as addition.
 
Physics news on Phys.org
The mean of a sum is the sum of the means. The terms in the sum do not have to be independent or have the same distribution.
 
mathman said:
The mean of a sum is the sum of the means. The terms in the sum do not have to be independent or have the same distribution.

Awesome, I wasn't sure. Thanks for clearing that up!
 

Thread 'Roulette wheel physics and probability'

Hi all, I've been a roulette player for more than 10 years (although I took time off here and there) and it's only now that I'm trying to understand the physics of the game. Basically my strategy in roulette is to divide the wheel roughly into two halves (let's call them A and B). My theory is that in roulette there will invariably be variance. In other words, if A comes up 5 times in a row, B will be due to come up soon. However I have been proven wrong many times, and I have seen some...
View full post »
Thread 'Detail of Diagonalization Lemma'

Thread 'Detail of Diagonalization Lemma'

The following is more or less taken from page 6 of C. Smorynski's "Self-Reference and Modal Logic". (Springer, 1985) (I couldn't get raised brackets to indicate codification (Gödel numbering), so I use a box. The overline is assigning a name. The detail I would like clarification on is in the second step in the last line, where we have an m-overlined, and we substitute the expression for m. Are we saying that the name of a coded term is the same as the coded term? Thanks in advance.
View full post »

Similar threads

I Randomly Stopped Sums vs the sum of I.I.D. Random Variables
Replies
2
Views
2K
I Statistical modeling and relationship between random variables
Replies
7
Views
2K
I Sampling theory and random sample
Replies
5
Views
2K
I Sample space, outcome, event, random variable, probability...
Replies
6
Views
3K
I Is this conditional expectation identity true?
Replies
1
Views
2K
MHB Distribution and Density functions of maximum of random variables
Replies
6
Views
4K
A Sum of independent random variables and Normalization
Replies
10
Views
3K
I IID and Dependent RVs: A Closer Look at their Relationship and Parameters
Replies
6
Views
1K
I Linear regression with error term
Replies
8
Views
2K
I On pdf of a sum of two r.v.s and differentiating under the integral
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top