# Can probability limit be used as mean for asymptotic distribution?

#### Mkkl

##### New Member
Hi there,

I was wondering the following. If I have found that a variable X converges to some probability limit p and subsequently I wish to find the asymptotic distribution of that variable, can I say that sqrt(N)(X - p) has an asymptotic normal distribution with mean zero and some covariance sigma?

I'm questioning this as the limit when n goes to infinity of E[X] is equal to the probability of X right, but how does it work the other way around?

Thanks,

Michael

#### BGM

##### TS Contributor
Convergence in probability does not implies it has a asymptotic normal distribution. You will need to check the underlying variable satisfy the requirement of, say some version of Central Limit Theorem.

Sorry I do not get the second paragraph of your inquiry.