Question

Let $X_1$ ... $X_n$ all be $p \times 1$ independent vectors. Let $E[X_i] = \mu_i$ and $Var(X_i) = \Sigma$. Let $\bar{X}$ be the elementwise average of the {$X_i$} (i.e. $\frac{1}{n} \sum_{i=1}^n X_i$). What is $Var(\bar{X})$ (check all that apply)? $\frac{1}{n^2} \sum_{i=1}^n Var(X_i)$ $\sum$ $\frac{1}{n^2} \sum$ $\frac{1}{n} \sum$ It can't be determined from the information given.

Name: let x1 xn all be p times 1 independent vectors let exi mui and varxi sigma let barx be the elementwise average of the xi ie frac1n sumi1n xi what is varbarx check all that apply frac 67075
Uploaded: 2023-07-05T04:32:32-08:00
Duration: 1 min 20 s
Channel: Madhur L
Description: let x1 xn all be p times 1 independent vectors let exi mui and varxi sigma let barx be the elementwise average of the xi ie frac1n sumi1n xi what is varbarx check all that apply frac 67075

          Let $X_1$ ... $X_n$ all be $p \times 1$ independent vectors. Let $E[X_i] = \mu_i$ and $Var(X_i) = \Sigma$. Let $\bar{X}$ be the elementwise average of the {$X_i$} (i.e. $\frac{1}{n} \sum_{i=1}^n X_i$). What is $Var(\bar{X})$ (check all that apply)?
$\frac{1}{n^2} \sum_{i=1}^n Var(X_i)$
$\sum$
$\frac{1}{n^2} \sum$
$\frac{1}{n} \sum$
It can't be determined from the information given.

$let x1 xn all be p times 1 independent vectors let exi mui and varxi sigma let barx be the elementwise average of the xi ie frac1n sumi1n xi what is varbarx check all that apply frac 67075$

Added by Luis P.

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