[SOLVED]Vector of I.I.D. RVs

OhMyMarkov

Member
Hello everyone!

Suppose $v$ is a vector of i.i.d. normal RV's with zero mean and standard deviation $\sigma$. Is the following true:

(1) $E[||v||^2]=\sigma ^2$
(2) $E[\sum _i v_i] = 0$

CaptainBlack

Well-known member
Hello everyone!

Suppose $v$ is a vector of i.i.d. normal RV's with zero mean and standard deviation $\sigma$. Is the following true:

(1) $E[||v||^2]=\sigma ^2$
(2) $E[\sum _i v_i] = 0$

$E\left(||v||^2\right)=E\left(\sum_i v_i^2 \right)=\sum_i E(v_i^2)=n\sigma^2$