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[SOLVED] Vector of I.I.D. RVs

OhMyMarkov

Member
Mar 5, 2012
83
Hello everyone! :D

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) $E[\sum _i v_i] = 0$

Thank you for your help!
 

CaptainBlack

Well-known member
Jan 26, 2012
890
Hello everyone! :D

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) $E[\sum _i v_i] = 0$

Thank you for your help!
\[E\left(||v||^2\right)=E\left(\sum_i v_i^2 \right)=\sum_i E(v_i^2)=n\sigma^2\]

Now do the same process of using the expectation of a sum is the sum of the expectations on the second.

CB