oh i didn't know that thanks.
I only knew $\displaystyle frac{f_{X}(x)}{f_{Y}(y)}$ is a cauchy distribution,
so the product of a cauchy distribution and a normal distribution has to get you back to a normal distribution?
[FONT=Lucida Grande]Assume two random variables X and Y are not independent,
[FONT=Lucida Grande]if P(X), P(Y) and P(Y|X) are all normal, then does P(X|Y) also can only be normal or not necessarily?
[FONT=Lucida Grande]thanks.
Thanks Chiro, just to confirm, so your argument still applies even if P(X) and P(Y) are not independent right,
so in conclusion,
Even if P(X) and P(Y) are not independent, if P(X), P(Y) and P(Y|X) are all normal, then P(X|Y) also has to be normal.
Anyone know answer to below.
If two random variables X and Y are both marginally normal, and conditional distribution of Y given any value of X is also normal.
Does this automatically mean the conditional distribution of X given any value of Y also has to be normal? or not necessarily.
sorry, maybe I should ask my question this way:
if we have y=1+dx+(dx)^2 in the limit of x->0, we ignore the term (dx)^2 and approximate y=1+dx, is this because the term (dx)^2 is too small relative to dx or is it because the term is just absolutely too small?
ie. if we have y=1+(dx)^2...
Quick question on high order term such as (dx)^2
in taylor expansion, higher order terms such as (dx)^2 is ignored because it's too small compared to the first order term...
if there is no first order term, can second order term still be ignored?
eg. if y=(dx)^2, do we always assume y=0...
Hi Viraltux,
the more I think about it, it does seem the only way of keeping marginal distribution of Y normal is for the normal conditional distributions of Y for each value of X follow the bivariate normal formula, with the mean shifting slightly and keeping variance the same.
As soon as...
cool Viraltux, just so that we are on the same page,
we agree that marginal normal distributions as a condition alone do not have to result in only bivariate normal.
but if we add an extra restriction that all conditional distributions are also normal, you are also not sure whether this...
Hi Viraltux,
I think in this case we are not actually doing a sum of normal distributions of independent random variables (which I agree would be normal).
What we are doing is superimposing the conditional normal distributions on each other to get to the marginal distribution of Y...
If you use that for the change of variance, I think the resultant marginal distribution of Y is no longer normal and would have very high kurtosis (more squeezed around the mean than a normal).
reason is:
If you think in the case of a proper bivariate normal distribution, for each X=x...
Hi Viraltux,
Can you please tell me within the sample simulation you made, what are the formulae for the change of the variance of the conditional normal distributions?
Thanks a lot!
Thanks viraltux, just to confirm my understanding, in your example:
"Imagine that given X=x the variance of the normal conditional distribution of Y is inversely proportional to x, and also imagine that the variance of X condition to Y=y is also inversely proportional to y.
Now you have X,Y...
In your example, I believe you are saying the conditional normal distributions having different variance? If that is the case, I don't see how the resultant marginal distribution (from adding all the conditional ones) can still be normal.
Doesn't the conditional distributions need to have the...
viraltux, your example doesn't work as it breaks one of the restrictions.
In your case, as soon as correlation is not zero (the mean of the normal conditional distributions shift), the resultant marginal distribution is no longer normal.
In fact, the more I think about it, it does seem the...