7. (6 points) A spider and y move along a straight line at times t = 0,1, . . .. The initial position of the y and the spider are integers. At each time period, the y moves one unit to the left with a probability p, one unit to the right with a probability p, and stays where it is with a probability 1 2;). The spider, knows the position of the y at the beginning of each period, and will always move one unit towards the y if its distance from the y is more than one unit. If the spider is one unit away from the y, it will either move one unit towards the y, or stay where it is. If the spider and the y land in the same position at the end of a period, then the spider captures the y, and the process terminates. The spider's objective is to capture the y in minimum expected number of steps. (a) Give a closed-form expression for the expected number of steps for capture when the spider is one unit away from the y. (b) Give a closed-form expression for the expected number of steps for capture when the spider is two units away from the y