Q:

How to find the mathematical expectation?

$190$ people take part in the marathon, and $124$ of them use the youth team of the university. The random value $\zeta$ is equal to the place of the best member of the university team. How to find the mathematical expectation of $\zeta$? 

A:

Of the competitors $66$ are not members of the university team.
For $i=1,\dots,66$ let random variable $X_{i}$ take value $1$ if
person $i$ gets a higher ranking then all members of the university
team and let $X_{i}$ take value $0$ otherwise.
Then: $$\zeta=1+\sum_{i=1}^{66}X_{i}$$
Now apply linearity of expectation and symmetry.

