Re: Statistical Indep and Corr of Normal RVs

This is from Wikipedia:

"It is sometimes mistakenly thought that one context in which
uncorrelatedness implies independence is when the random variables
involved are normally distributed. Here are the facts:

* Suppose two random variables X and Y are jointly normally
distributed. That is the same as saying that the random vector (X, Y)
has a multivariate normal distribution. It means that the joint
probability distribution of X and Y is such that for any two constant
(i.e., non-random) scalars a and b, the random variable aX + bY is
normally distributed. In that case if X and Y are uncorrelated, i.e.,
their covariance cov(X, Y) is zero, then they are independent.

* But it is possible for two random variables X and Y to be so
distributed jointly that each one alone is normally distributed, and
they are uncorrelated, but they are not independent. Examples appear
below...."

This last statement though seems to directly contradict yours (which I
will paraphrase a bit as):
"But ZERO correlation implies independence IF and ONLY IF the random
variables are Normal meaning each is a univariate Normal r.v."

Can you see the source of confusion?
Matt

.

Relevant Pages

  • Re: Normal Random Variable Generator
    ... Excel, PowerPoint, and VBA add-ins, tutorials ... > random variables in Excel: ... > differ from a normal distribution. ... but I don't know how to use in my VBA code. ...
    (microsoft.public.excel.programming)
  • Re: jointly gaussian
    ... variables with normal distribution? ... if two random variables have a bivariate normal ... point leads me to suspect that you mean something else by the ... phrase "independent of each other" ...
    (comp.dsp)
  • Re: Distribution of random sum of random variables
    ... Eric Wong wrote: ... N is a discrete nonnegative random variable ... >following random sum converges to the normal distribution? ...
    (sci.math)
  • Re: jointly gaussian
    ... quality and helpful! ... If one comes across a jointly normal distribution, ... if two random variables have a bivariate normal ...
    (comp.dsp)