Suppose that we have a long and thin tube. All bacterial at t = 0 are at the center of the tube i.e., all bacterial at t = 0 are at r = 0. The bacterial can move from both directions(left or right). Suppose that each run moves the bacterium a distance & along the tube and each bacterium moves left with probability p and right with probability 1 -p at each run. Let E(xx) denote the average position the bacterium after k runs. (a) Find an expression for E(TK) in terms of k, p and e. (b) Find an expression for the variance of Tx i.e. find E(x}) - (E(C))