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.

  • $\begingroup$ 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

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