Let $X_n$ a random variable of same law

[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

 

[Feynman]

Hello

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

 

[recon]

Feynman, LaTex is down at the moment.

 

[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.