# Find Expected Value, Variance, and Limit of Uniform Distribution

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.

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