All ships travel at the same speed through a wide canal. Each ship takes days to traverse the length of the canal. Eastbound ships $($i$.$e$.,$ ships traveling east$)$ arrive as a Poisson process with an arrival rate of ships per day. Westbound ships $($i$.$e$.,$ ships traveling west$)$ arrive as an independent Poisson process with an arrival rate of ships per day. A pointer at some location in the canal is always pointing in the direction of travel of the most recent ship to pass it$.$

In each part below, your answers will be algebraic expressions in terms of and$/$or $.$ Enter $"$LE$"$ for and $"$LW$"$ for $,$ and use "exp$()"$ for exponentials. Do not use "fac$()"$ or $"!"$ for factorials; instead, calculate out the numerical value of any factorials. Follow standard notation.