Problem 2 (10 points) A logger takes an exponential amount of time to cut a log with mean 2.0. He tosses the log on a pile. Once there are 5 logs on the pile, he drags it away (this takes the logger an exponentially distributed amount of time with mean 10.0) and the next log starts a new pile. 1. Draw a rate diagram for this system. (4pt) 2. Find the long run probability that the logger is engaged in log cutting, not dragging. (3pt for the equations, 2pt for the solution) 3. Find the mean time to build a pile of 5 logs starting from 0 logs. (1pt) Problem 2 (10 points) A logger takes an exponential amount of time to cut a log with mean 2.0. He tosses the log on a pile. Once there are 5 logs on the pile, he drags it away (this takes the logger an exponentially distributed amount of time with mean 10.0) and the next log starts a new pile. 1. Draw a rate diagram for this system. (4pt) 2. Find the long run probability that the logger is engaged in log cutting, not dragging. (3pt for the equations, 2pt for the solution) 3. Find the mean time to build a pile of 5 logs starting from 0 logs. (1pt)