(1) Sophia the bug is now in the middle of the chess board, and now every second she moves either east im.n)->(m+1,n) or

[answerhappygod]

1 Sophia The Bug Is Now In The Middle Of The Chess Board And Now Every Second She Moves Either East Im N M 1 N Or 1 (67.73 KiB) Viewed 79 times

(1) Sophia the bug is now in the middle of the chess board, and now every second she moves either east im.n)->(m+1,n) or west (m.)->(m-1,n). [Ignore the edges, perhaps by letting the chess board go on forever in all directions (1a) What are all of the places she can be after 5 seconds? [lt may be useful to label her new starting place as (0,0).) (16) If Sophia flips a [fair] coin to decide whether to go east (heads) or west (tails) each second, what is the probability that she will end up at each location from part 1? (10) What is Sophia's average displacement from her starting position in this part of the story? (10) How would this average displacement change if Sophia's coin is not fair, giving heads 60% of the time and tails 40% of the time? [lt will definitely move east; the task is to quantify that shift.]