Sum of random number of variables

Let \(x_1,x_2,x_3, \ldots \) be sequence of numbers randomly picked from the interval \([0,1]\) with uniform distribution. define \[S=x_1+\cdots+x_n\mid x_1+\cdots +x_{n}\geq 1 \land x_1+\cdots+x_{n-1}<1.\]

The expected value \(E\left[S\right]\) can be written as \(\dfrac{ae}{b}\), where \(a\) and \(b\) are coprime integers. Find \(a+b\)


Inspiration 1 and Inspiration 2.

×

Problem Loading...

Note Loading...

Set Loading...