Suppose that an object can be at any one ofn+1 equally spaced points xq, X|,... , x. When an object is at location x,-, it is equally likely to move to either x,_i or x,+i and cannot directly move to any other location. Consider the probabilities {P, }"=o that an object starting at location x,- will reach the left endpoint xq before reaching the right endpoint x. Clearly, Pq I and Pn 0. Since the object can move to x, only from x,_| or xI+i and does so with probability \ for each of these locations, P, = if,-. 1 2 for each / = 1, 2,... , n 1. a. Show that 1 0-. 0 1 -h2-. 1_ 2 '. I 0 -k 1 - ' Pi ' r 1 2 P2 0 . Pn-I . . 0 _ b. Solve this system using n 10, 50, and 100. c. Change the probabilities to a and 1 a for movement to the left and right, respectively, and derive the linear system similar to the one in part (a). d. Repeat part (b) with a = |
MGF 1107 Pre-Class Assignment 2A/2B Read through sections 2A and 2B in your book and answer the following questions. 1) Define: a) unit - A quantity used as a standard of measurement b) unit analysis - is a method used to convert from one unit of measure to another 2) Why do you think we need units when keeping track of real-life numbers Units help us measure certain things such as distances, weight, and heights of different things. 3) What does the word ‘per’ imply in mathematical problems It means “for every.” 4) What does the word ‘of’ imply in mathematical problems “Of” is used in multiplication 5) Give one example from the US customary system and the international metric system for
