Random Walks  by Mitch Owens

    Random Walks is where you find how many blocks you can change position by using a two sided coin.  By using a coin you can find the probability of the direction of  movement by moving steps forward.

    By using Pascal's Triangle you can find the average number of movements for a certain number of flips. Each row on Pascal's triangle represents another row of Flips such as when the triangle starts the rows are:

1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

    These are the first five rows of the triangle each can be taken to figure out how to  find average distance in the steps taken.

    The walks could be for a 10 step random walk

                    -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

    In the walk the most steps taken remain at 0, and as you continue the walk each spot 2, 4, 6, 8, 10 each have progressively lower probabilities.

    Then you cannot have a odd number on an even number of flips, but you can end on an odd number if you have an odd number of flips in your walk.  Therefore each can represent a different amount of steps.