- Thread starter
- Moderator
- #1

- Jan 26, 2012

- 995

-----

**Problem**: Let $X_1,X_2,\ldots X_n$ be i.i.d. exponential random variables. Show that the probability that the largest of them is greater than the sum of the others is $n/2^{n-1}$. That is, if $M=\max\limits_j X_j$ then show that

\[P\left\{ M > \sum_{i=i}^n X_i - M\right\} = \frac{n}{2^{n-1}}\]

-----

**Hint**:

What is $\displaystyle P\left(X_1 > \sum_{i=2}^n X_i\right)$?

Remember to read the POTW submission guidelines to find out how to submit your answers!