Variables and normal distributions

AI Thread Summary
The discussion centers on the relationship between two independent normally distributed variables, u and v, both with a mean of 0 and variance a^2. It is clarified that the expected value of the product uv is not a^2 if u and v are independent; rather, it is zero due to the symmetry of the normal distribution. Participants confirm that the expected value of the product of two independent normal variables with zero mean is indeed zero. The conversation concludes with an acknowledgment of this conclusion.
ebrattr
Messages
16
Reaction score
0
Hi everyone,
I would like to know if this stament is true or not. I have two variables u,v both of them distributed as normal distribution with mean 0 and variance a^2. Is it true that the expected value of uv is a^2 ?
Thanks
 
Physics news on Phys.org
If u and v are independent, this is not true.
Just consider the symmetry of the system.
 
Yeahhh... its cero. Thanks.
 

Thread 'Please Explain (actually explain) The Monty Hall Problem'

Hello, I'm joining this forum to ask two questions which have nagged me for some time. They both are presumed obvious, yet don't make sense to me. Nobody will explain their positions, which is...uh...aka science. I also have a thread for the other question. But this one involves probability, known as the Monty Hall Problem. Please see any number of YouTube videos on this for an explanation, I'll leave it to them to explain it. I question the predicate of all those who answer this...
View full post »

Thread 'Value of intuitionistic logic'

I'm taking a look at intuitionistic propositional logic (IPL). Basically it exclude Double Negation Elimination (DNE) from the set of axiom schemas replacing it with Ex falso quodlibet: ⊥ → p for any proposition p (including both atomic and composite propositions). In IPL, for instance, the Law of Excluded Middle (LEM) p ∨ ¬p is no longer a theorem. My question: aside from the logic formal perspective, is IPL supposed to model/address some specific "kind of world" ? Thanks.
View full post »

Thread 'Formal derivation of statement from Peano Arithmetic system'

I was reading a Bachelor thesis on Peano Arithmetic (PA). PA has the following axioms (not including the induction schema): $$\begin{align} & (A1) ~~~~ \forall x \neg (x + 1 = 0) \nonumber \\ & (A2) ~~~~ \forall xy (x + 1 =y + 1 \to x = y) \nonumber \\ & (A3) ~~~~ \forall x (x + 0 = x) \nonumber \\ & (A4) ~~~~ \forall xy (x + (y +1) = (x + y ) + 1) \nonumber \\ & (A5) ~~~~ \forall x (x \cdot 0 = 0) \nonumber \\ & (A6) ~~~~ \forall xy (x \cdot (y + 1) = (x \cdot y) + x) \nonumber...
View full post »

Similar threads

I Normality of errors and residuals in ordinary linear regression
Replies
3
Views
2K
I What is the expected (squared) coefficient of variation of a sample?
Replies
6
Views
3K
A A different discrete normal distribution
Replies
2
Views
2K
I Relating Moments from one Distribution to the Moments of Another
Replies
7
Views
2K
I Desirable estimator properties...
Replies
7
Views
2K
I Linear regression and random variables
Replies
30
Views
4K
I Citation needed: Only multivariate rotationally invariant distribution with iid components is a multivariate normal distribution
Replies
3
Views
2K
I Help me understand skewness in QQ-plots please
Replies
1
Views
1K
A Estimation error from estimation quantile of normal distribution
Replies
3
Views
2K
I How to show these random variables are independent?
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top