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#### OhMyMarkov

##### Member

- Mar 5, 2012

- 83

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!

- Thread starter OhMyMarkov
- Start date

- Thread starter
- #1

- Mar 5, 2012

- 83

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!

- Jan 26, 2012

- 890

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

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!

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

CB