4. (5 marks) Consider the grid below. Suppose that starting at point S you can go one step up or one step to the right at each move. This is continued until the point labeled F is reached. All paths from S to F are equally likely. On your random journey you must pay $10 if you pass through point A, $5 if you pass through B, $3 if you pass through point C, and $6 if you pass through point D. Let the random variable Y be the total cost to travel from S to F. What is the expected value of Y. F S