suppose if the particle jumps to the right, and if it jumps to the left..
so
If is the position of the particle after n jumps, you have:
now find
Suppose that a particle starts at the origin of the real line and moves along the line in jumps of one unit. For each jump, the probability is that the particle will jump one unit to the left and the probability is that the particle will jump one unit to the right. Find the expected value of the position of the particle after jumps.