# Limit in probability of (x-bar)^2 ?

#### haml.kn

##### New Member
Anyone have any idea how to prove or show what the limit in probability of (x-bar)^2 is?

sample is drawn from CDF F(x)=1-x^-4

#### BGM

##### TS Contributor
Do you mean the sample variance will converge in probability to which quantity?

#### haml.kn

##### New Member
I suppose that is the idea right that the variation between the sample statistics and the population parameter is 0. I'm just not sure how to show what the actual limit in probability is of (x-bar)^2 and if the information about the CDF is relevant to finding the limit in probability

#### ANDS!

##### New Member
It may be more complex than this, but I'm not sure why you can't use the CDF to find the mean of the distribution and - armed with that - simply use the CMT to determine what the the sample mean squared converges to.