Let random variables \( \{ X_r : r \geq 1 \} \) be independent and uniformly distributed on \( [0, 1] \). Let \( 0 < x < 1 \) and define a random variable
\[
N = \min \{ n \geq 1 : X_1 + X_2 + \cdots + X_n > x \}.

\]

Find the mean and variance of \( N \).

The best solution was submitted by 김호진, 09학번. Congratulations!

Similar solutions were also submitted by 라준현(08학번, +3), 서기원(09학번, +3), 김범수(10학번, +3), 황성호(13학번, +3), 어수강(서울대, +3), 이시우(POSTECH, +3), Fardad Pouran(Sharif University of Tech, Iran, +3), 양지훈(10학번, +2), 이정민(서울대, +2). Thank you for your participation.

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studentCategory가 problem으로 되어 있습니다.

Fardad PouranHello Dear Professor and Students,

I wanted to ask am I allowed to participate here as I am from Sharif University of Technology(, Tehran, Iran) ?

It will be my honor to participate .

감사합니다 🙂

Sincerely,

F. Pouran

Ji Oon LeePost author지적 감사합니다. 수정했습니다.

Ji Oon LeePost authorYour are more than welcome to participate the problem of the week. Thank you for your participation.