0
$\begingroup$

Let $X_1, X_2, \ldots, X_n$ be a sequences of independent random variables. $X_i \sim U(0, 2A)$.

Compute $E(X_i)$ and the $Var(X_i)$. Also compute the $lim_{n\to\infty} P(X_1, X_2, \ldots , X_n > na + x\sqrt{b})$.

I found the expected value and variance to be $E(X_i) = a $ and $Var(X_i) = a^2/3 $. I'm having trouble solving the limit.

$\endgroup$
  • $\begingroup$ What are $a,b,x$? Arbitrary? $\endgroup$ – Ian May 11 '16 at 0:11
  • $\begingroup$ Is there a sum of those variables in the limit or something? $\endgroup$ – Batman May 11 '16 at 0:14
  • $\begingroup$ as written, the probabilty will drop to zero as soon as $n>2$ $\endgroup$ – user237392 May 11 '16 at 0:17

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.