TITLE: Expected number of frog jumps
QUESTION [7 upvotes]: There is frog jumping forward on a line. Each jump distance is random with a known cumulative distribution function $F$. What is the expected number of jumps to reach (or go beyond) distance $d$ from the origin?
If there is a Wikipedia or other web page describing the formula in terms of $F$, just give a (deep) link. I'd prefer to have the proof as well.

REPLY [4 votes]: Reference: This problem has been worked out thoroughly if the random walk steps are uniform and continuous. See, for example,

Russell, K. G. On the number of uniform random variables which must be added to exceed a given level.
  J. Appl. Probab. 20 (1983), no. 1, 172–177. 

It is a well-known puzzle to show that the expected number of uniform(0,1) steps 
to exceed level 1 is $\exp(1)$. I was sure that this appears somewhere on this site, but I can't find it.