Simple random walk

Could anyone explain that how in order to get from i to j in n steps the random walk must make 1/2(n+j-i ) steps in an upward direction and n-u in a downward direction in simple random walk? (Chapter 3 Section 5.3 )


Thanks,

anjali

 

If number of up steps =u ,the number of down steps n-u (total =n)

Code:

current position  + up steps - down steps = new position
i                        + u           - (n-u)           = j

 

thank you for reply