Traffic on a one way road follows a rate λ Poisson process (this means that cars arrive with rate λ per minute). A turtle needs c minutes to cross the road, so she will need a gap of at...

Traffic on a one way road follows a rate λ Poisson process (this means that cars arrive with rate λ per minute). A turtle needs c minutes to cross the road, so she will need a gap of at least c minutes to cross. Suppose that the turtle can see far ahead, so she can decide whether it is safe to cross the road or not. Let R denote the time the turtle spends waiting by the road after her arrival before starting to cross the road. Find E[R].