Distribution until the First Increase?
On a homework I've been given this problem. I don't even know where to start. Is there a name for this distribution or a way I can look up more information about it? Thanks!
Let be independent identically distributed continous random variables. We call the first time of increase if
Let be the time until the first increase. Show that .
The hint we were given was to use the tail sum formula for a random variable taking values in the positive integers. But how do you go from a discrete formula to a continuous one? I am completely lost. What is this distribution called?