Let $X_n$ a random variable of same law

1. Sep 14, 2004

Feynman

Hello

I have a simple question :
Let $X_n$ a random variable of same law
If $V(X_n)\longrightarrow 0$ when $n\longrightarrow +\infty$
How schow that : $E(X_n)\longrightarrow C$ and $E(X_{n}^{2}\longrightarrow C^2$ and C is a constant?
Thanks

2. Sep 14, 2004

Feynman

Hello

$$I have a simple question : Let X_n a random variable of same law If V(X_n)\longrightarrow 0 when n\longrightarrow +\infty How schow that : E(X_n)\longrightarrow C and E(X_{n}^{2}\longrightarrow C^2 and C is a constant? Thanks$$

3. Sep 14, 2004

recon

Feynman, LaTex is down at the moment.

4. Sep 15, 2004

uart

How far have you got with this one Feynman?

I suggest you let z = x - E(x) and then prove that E( z^2 ) = 0 implies that Z has a discrete probability denstiy with P(z=0) = 1.