# Solution: 2013-10 Mean and variance of random variable

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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## 4 thoughts on “Solution: 2013-10 Mean and variance of random variable”

1. student

Category가 problem으로 되어 있습니다.

2. Fardad Pouran

Hello 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

3. Ji Oon Lee Post author

지적 감사합니다. 수정했습니다.

4. Ji Oon Lee Post author

Your are more than welcome to participate the problem of the week. Thank you for your participation.