A computer program generates 1000 iid numbers in the range of minus to plus inifity. It then randomly displays 1 number that was generated and asks you if its the highest number, and you answer Yes or No.

If you answer No, it will show you the next number in the list and ask if that is the highest number.

If you answer Yes to the number generated being the largest, it will then display all the remaining numbers so you can see.

So what is the optimal time to choose a number, and what is the probility of selecting correctly?

So if Y is a number that is generated, its $\displaystyle Y~U(-\infty, \infty)$ and 1000 Y's are generated. So you want the order statistic that is $\displaystyle Y_{(n)}: max \{ y_1,y_2...,y_n \}$

so Im just nto sure how to formulate the order statistic distribution?