-1
$\begingroup$

Let $$Z_n=\frac{\sum{W_i}}{\sqrt{n}\sigma}\sim N(0,1),$$ where $W_i=X_i-\mu$. What are the mean and variance of $W_i$?

$\endgroup$

closed as off-topic by NCh, Saad, Lee David Chung Lin, Leucippus, Eevee Trainer Mar 22 at 4:31

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – NCh, Saad, Lee David Chung Lin, Leucippus, Eevee Trainer
If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ Do you know the distribution of $X_i$? $\endgroup$ – Minus One-Twelfth Mar 21 at 22:36
  • 1
    $\begingroup$ It is a distribution $F_x$ with finite $E(X)=\mu$ and $Var(X)=\sigma^2>0$ $\endgroup$ – theQuestion Mar 21 at 22:40
0
$\begingroup$

$\newcommand{\Var}{\operatorname{Var}}\newcommand{\E}{\mathbb{E}}$The mean of $W_i$ is $0$ and variance of $W_i$ is same as that of $X_i$, namely $\sigma^2$. This follows from standard properties of mean and variance ($\E(X-c) = \E(X)-c$ and $\Var(X-c)= \Var(X)$, for any constant $c$).

$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.