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 p that the particle will move one unit to the left and the probability is 1-p that the particle will jump one unit to the right. Jumps are independent of one another. Ultimately, we are going to be concerned with the position of the particle after n jumps. (a) Let Y; be the change in position after jump number i. What is the pmf of Y/? Hint: You may want to write Y, as a function of a Z - Bernoulli(p) (b) Write X, in terms of the Y. (or 2; if you prefer) (c) Compute ELXn] (d) Compute Var{ X..)