Problem 2 The diffusion of electrons and holes across a potential barrier in an electronic device...
A total of 5 balls of two possible colours, black and white, have been put into a box. A ball is chosen uniformly at random. If the ball is black, we replace this ball in the box with a white ball. Similarly, if the ball chosen is white, we replace this ball in the box with a black one. Let {Xn,n 2 0) denote the number of white balls in the box after the n-th trial. This defines a Markov...
A total of 5 balls of two possible colours, black and white, have been put into a box. A ball is chosen uniformly at random. If the ball is black, we replace this ball in the box with a white ball. Similarly, if the ball chosen is white, we replace this ball in the box with a black one. Let {Xn,n 2 0) denote the number of white balls in the box after the n-th trial. This defines a Markov...
(25) A game has two boxes as follows: Box A initially contains 2 white balls Box B initially contains 3 red balls. At each step in the game, 1 ball is selected at random from each box and the 2 balls are interchanged. Thus, Box A always contains 2 balls, and Box B always contains 3 balls. The game continues indefinitely. The game may be described by a Markov chain having three states: S0,S1,S2, whose subscript denotes the number of...
Experience has shown that the general mood of Henry may be realistically modeled as a three-state Markov process with the mutually exclusive collectively exhaustive states: State 1: Cheerful State 2: So-so State 3: Glum His mood can change only overnight and the following transition probabilities apply to each night’s trial: 0.0 0.3 0.7 0.3 0.4 0.3 0.6 0.2 0.2 P 1 2 3 1 2 3 Problem 10 Three...