To graph: The transition diagram for Markov process, if Heather and Blake play a card game in which they take turns drawing a card from a shuffled deck of 52 cards, Heather wins the game if she draws a hurt and Blake wins the game if he draws s black card. Where, if a player does not win on their turns then card is return to the deck and then deck is shuffled and it becomes the turn of other player, where the game has four states: Heather wins, Blake wins, Heather’s turn and Blake’s turns.

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Answer 1

Question

Chapter 8.3, Problem 24E

(a)

To determine

To graph: The transition diagram for Markov process, if Heather and Blake play a card game in which they take turns drawing a card from a shuffled deck of 52 cards, Heather wins the game if she draws a hurt and Blake wins the game if he draws s black card. Where, if a player does not win on their turns then card is return to the deck and then deck is shuffled and it becomes the turn of other player, where the game has four states: Heather wins, Blake wins, Heather’s turn and Blake’s turns.

(b)

To determine

To calculate: The absorbing stochastic matrix for the Markov process, if Heather and Blake play a card game in which they take turns drawing a card from a shuffled deck of 52 cards, Heather wins the game if she draws a hurt and Blake wins the game if he draws s black card. Where, if a player does not win on their turns then card is return to the deck and then deck is shuffled and it becomes the turn of other player, where the game has four states: Heather wins, Blake wins, Heather’s turn and Blake’s turns.

(c)

To determine

To calculate: The stable matrix, if Heather and Blake play a card game in which they take turns drawing a card from a shuffled deck of 52 cards, Heather wins the game if she draws a hurt and Blake wins the game if he draws s black card. Where, if a player does not win on their turns then card is return to the deck and then deck is shuffled and it becomes the turn of other player, where the game has four states: Heather wins, Blake wins, Heather’s turn and Blake’s turns.

(d)

To determine

To calculate: The probability that Heather wins if she got first, if Heather and Blake play a card game in which they take turns drawing a card from a shuffled deck of 52 cards, Heather wins the game if she draws a hurt and Blake wins the game if he draws s black card. Where, if a player does not win on their turns then card is return to the deck and then deck is shuffled and it becomes the turn of other player, where the game has four states: Heather wins, Blake wins, Heather’s turn and Blake’s turns.

(e)

To determine

To calculate: The expected number of turns if heather got first, if Heather and Blake play a card game in which they take turns drawing a card from a shuffled deck of 52 cards, Heather wins the game if she draws a hurt and Blake wins the game if he draws s black card. Where, if a player does not win on their turns then card is return to the deck and then deck is shuffled and it becomes the turn of other player, where the game has four states: Heather wins, Blake wins, Heather’s turn and Blake’s turns.

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Module Code: MATH380202 3. (a) Let {} be a white noise process with variance σ2. Define an ARMA(p,q) process {X} in terms of {+} and state (without proof) conditions for {X} to be (i) weakly stationary and (ii) invertible. Define what is meant by an ARIMA (p, d, q) process. Let {Y} be such an ARIMA(p, d, q) process and show how it can also be represented as an ARMA process, giving the AR and MA orders of this representation. (b) The following tables show the first nine sample autocorrelations and partial auto- correlations of X and Y₁ = VX+ for a series of n = 1095 observations. (Notice that the notation in this part has no relationship with the notation in part (a) of this question.) Identify a model for this time series and obtain preliminary estimates for the pa- rameters of your model. X₁ = 15.51, s² = 317.43. k 1 2 3 4 5 6 7 Pk 0.981 0.974 0.968 akk 0.981 0.327 8 9 0.927 0.963 0.957 0.951 0.943 0.935 0.121 0.104 0.000 0.014 -0.067 -0.068 -0.012 Y₁ = VX : y = 0.03, s² = 11.48. k 1…

Answer 2

Question

Chapter 8.3, Problem 24E

(a)

To determine

To graph: The transition diagram for Markov process, if Heather and Blake play a card game in which they take turns drawing a card from a shuffled deck of 52 cards, Heather wins the game if she draws a hurt and Blake wins the game if he draws s black card. Where, if a player does not win on their turns then card is return to the deck and then deck is shuffled and it becomes the turn of other player, where the game has four states: Heather wins, Blake wins, Heather’s turn and Blake’s turns.

(b)

To determine

To calculate: The absorbing stochastic matrix for the Markov process, if Heather and Blake play a card game in which they take turns drawing a card from a shuffled deck of 52 cards, Heather wins the game if she draws a hurt and Blake wins the game if he draws s black card. Where, if a player does not win on their turns then card is return to the deck and then deck is shuffled and it becomes the turn of other player, where the game has four states: Heather wins, Blake wins, Heather’s turn and Blake’s turns.

(c)

To determine

To calculate: The stable matrix, if Heather and Blake play a card game in which they take turns drawing a card from a shuffled deck of 52 cards, Heather wins the game if she draws a hurt and Blake wins the game if he draws s black card. Where, if a player does not win on their turns then card is return to the deck and then deck is shuffled and it becomes the turn of other player, where the game has four states: Heather wins, Blake wins, Heather’s turn and Blake’s turns.

(d)

To determine

To calculate: The probability that Heather wins if she got first, if Heather and Blake play a card game in which they take turns drawing a card from a shuffled deck of 52 cards, Heather wins the game if she draws a hurt and Blake wins the game if he draws s black card. Where, if a player does not win on their turns then card is return to the deck and then deck is shuffled and it becomes the turn of other player, where the game has four states: Heather wins, Blake wins, Heather’s turn and Blake’s turns.

(e)

To determine

To calculate: The expected number of turns if heather got first, if Heather and Blake play a card game in which they take turns drawing a card from a shuffled deck of 52 cards, Heather wins the game if she draws a hurt and Blake wins the game if he draws s black card. Where, if a player does not win on their turns then card is return to the deck and then deck is shuffled and it becomes the turn of other player, where the game has four states: Heather wins, Blake wins, Heather’s turn and Blake’s turns.

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Answer 3

Question

Chapter 8.3, Problem 24E

(a)

To determine

To graph: The transition diagram for Markov process, if Heather and Blake play a card game in which they take turns drawing a card from a shuffled deck of 52 cards, Heather wins the game if she draws a hurt and Blake wins the game if he draws s black card. Where, if a player does not win on their turns then card is return to the deck and then deck is shuffled and it becomes the turn of other player, where the game has four states: Heather wins, Blake wins, Heather’s turn and Blake’s turns.

(b)

To determine

To calculate: The absorbing stochastic matrix for the Markov process, if Heather and Blake play a card game in which they take turns drawing a card from a shuffled deck of 52 cards, Heather wins the game if she draws a hurt and Blake wins the game if he draws s black card. Where, if a player does not win on their turns then card is return to the deck and then deck is shuffled and it becomes the turn of other player, where the game has four states: Heather wins, Blake wins, Heather’s turn and Blake’s turns.

(c)

To determine

To calculate: The stable matrix, if Heather and Blake play a card game in which they take turns drawing a card from a shuffled deck of 52 cards, Heather wins the game if she draws a hurt and Blake wins the game if he draws s black card. Where, if a player does not win on their turns then card is return to the deck and then deck is shuffled and it becomes the turn of other player, where the game has four states: Heather wins, Blake wins, Heather’s turn and Blake’s turns.

(d)

To determine

To calculate: The probability that Heather wins if she got first, if Heather and Blake play a card game in which they take turns drawing a card from a shuffled deck of 52 cards, Heather wins the game if she draws a hurt and Blake wins the game if he draws s black card. Where, if a player does not win on their turns then card is return to the deck and then deck is shuffled and it becomes the turn of other player, where the game has four states: Heather wins, Blake wins, Heather’s turn and Blake’s turns.

(e)

To determine

To calculate: The expected number of turns if heather got first, if Heather and Blake play a card game in which they take turns drawing a card from a shuffled deck of 52 cards, Heather wins the game if she draws a hurt and Blake wins the game if he draws s black card. Where, if a player does not win on their turns then card is return to the deck and then deck is shuffled and it becomes the turn of other player, where the game has four states: Heather wins, Blake wins, Heather’s turn and Blake’s turns.

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Answer 4

Question

Chapter 8.3, Problem 24E

(a)

To determine

To graph: The transition diagram for Markov process, if Heather and Blake play a card game in which they take turns drawing a card from a shuffled deck of 52 cards, Heather wins the game if she draws a hurt and Blake wins the game if he draws s black card. Where, if a player does not win on their turns then card is return to the deck and then deck is shuffled and it becomes the turn of other player, where the game has four states: Heather wins, Blake wins, Heather’s turn and Blake’s turns.

(b)

To determine

To calculate: The absorbing stochastic matrix for the Markov process, if Heather and Blake play a card game in which they take turns drawing a card from a shuffled deck of 52 cards, Heather wins the game if she draws a hurt and Blake wins the game if he draws s black card. Where, if a player does not win on their turns then card is return to the deck and then deck is shuffled and it becomes the turn of other player, where the game has four states: Heather wins, Blake wins, Heather’s turn and Blake’s turns.

(c)

To determine

To calculate: The stable matrix, if Heather and Blake play a card game in which they take turns drawing a card from a shuffled deck of 52 cards, Heather wins the game if she draws a hurt and Blake wins the game if he draws s black card. Where, if a player does not win on their turns then card is return to the deck and then deck is shuffled and it becomes the turn of other player, where the game has four states: Heather wins, Blake wins, Heather’s turn and Blake’s turns.

(d)

To determine

To calculate: The probability that Heather wins if she got first, if Heather and Blake play a card game in which they take turns drawing a card from a shuffled deck of 52 cards, Heather wins the game if she draws a hurt and Blake wins the game if he draws s black card. Where, if a player does not win on their turns then card is return to the deck and then deck is shuffled and it becomes the turn of other player, where the game has four states: Heather wins, Blake wins, Heather’s turn and Blake’s turns.

(e)

To determine

To calculate: The expected number of turns if heather got first, if Heather and Blake play a card game in which they take turns drawing a card from a shuffled deck of 52 cards, Heather wins the game if she draws a hurt and Blake wins the game if he draws s black card. Where, if a player does not win on their turns then card is return to the deck and then deck is shuffled and it becomes the turn of other player, where the game has four states: Heather wins, Blake wins, Heather’s turn and Blake’s turns.

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Answer 5

Chapter 8.3, Problem 24E

(a)

To determine

To graph: The transition diagram for Markov process, if Heather and Blake play a card game in which they take turns drawing a card from a shuffled deck of 52 cards, Heather wins the game if she draws a hurt and Blake wins the game if he draws s black card. Where, if a player does not win on their turns then card is return to the deck and then deck is shuffled and it becomes the turn of other player, where the game has four states: Heather wins, Blake wins, Heather’s turn and Blake’s turns.

(b)

To determine

To calculate: The absorbing stochastic matrix for the Markov process, if Heather and Blake play a card game in which they take turns drawing a card from a shuffled deck of 52 cards, Heather wins the game if she draws a hurt and Blake wins the game if he draws s black card. Where, if a player does not win on their turns then card is return to the deck and then deck is shuffled and it becomes the turn of other player, where the game has four states: Heather wins, Blake wins, Heather’s turn and Blake’s turns.

(c)

To determine

To calculate: The stable matrix, if Heather and Blake play a card game in which they take turns drawing a card from a shuffled deck of 52 cards, Heather wins the game if she draws a hurt and Blake wins the game if he draws s black card. Where, if a player does not win on their turns then card is return to the deck and then deck is shuffled and it becomes the turn of other player, where the game has four states: Heather wins, Blake wins, Heather’s turn and Blake’s turns.

(d)

To determine

To calculate: The probability that Heather wins if she got first, if Heather and Blake play a card game in which they take turns drawing a card from a shuffled deck of 52 cards, Heather wins the game if she draws a hurt and Blake wins the game if he draws s black card. Where, if a player does not win on their turns then card is return to the deck and then deck is shuffled and it becomes the turn of other player, where the game has four states: Heather wins, Blake wins, Heather’s turn and Blake’s turns.

(e)

To determine

To calculate: The expected number of turns if heather got first, if Heather and Blake play a card game in which they take turns drawing a card from a shuffled deck of 52 cards, Heather wins the game if she draws a hurt and Blake wins the game if he draws s black card. Where, if a player does not win on their turns then card is return to the deck and then deck is shuffled and it becomes the turn of other player, where the game has four states: Heather wins, Blake wins, Heather’s turn and Blake’s turns.

Answer 6

Chapter 8.3, Problem 24E

(a)

To determine

To graph: The transition diagram for Markov process, if Heather and Blake play a card game in which they take turns drawing a card from a shuffled deck of 52 cards, Heather wins the game if she draws a hurt and Blake wins the game if he draws s black card. Where, if a player does not win on their turns then card is return to the deck and then deck is shuffled and it becomes the turn of other player, where the game has four states: Heather wins, Blake wins, Heather’s turn and Blake’s turns.

Answer 7

Chapter 8.3, Problem 24E

(a)

To determine

To graph: The transition diagram for Markov process, if Heather and Blake play a card game in which they take turns drawing a card from a shuffled deck of 52 cards, Heather wins the game if she draws a hurt and Blake wins the game if he draws s black card. Where, if a player does not win on their turns then card is return to the deck and then deck is shuffled and it becomes the turn of other player, where the game has four states: Heather wins, Blake wins, Heather’s turn and Blake’s turns.

Answer 8

(b)

To determine

To calculate: The absorbing stochastic matrix for the Markov process, if Heather and Blake play a card game in which they take turns drawing a card from a shuffled deck of 52 cards, Heather wins the game if she draws a hurt and Blake wins the game if he draws s black card. Where, if a player does not win on their turns then card is return to the deck and then deck is shuffled and it becomes the turn of other player, where the game has four states: Heather wins, Blake wins, Heather’s turn and Blake’s turns.

Answer 9

(b)

To determine

To calculate: The absorbing stochastic matrix for the Markov process, if Heather and Blake play a card game in which they take turns drawing a card from a shuffled deck of 52 cards, Heather wins the game if she draws a hurt and Blake wins the game if he draws s black card. Where, if a player does not win on their turns then card is return to the deck and then deck is shuffled and it becomes the turn of other player, where the game has four states: Heather wins, Blake wins, Heather’s turn and Blake’s turns.

Answer 10

(c)

To determine

To calculate: The stable matrix, if Heather and Blake play a card game in which they take turns drawing a card from a shuffled deck of 52 cards, Heather wins the game if she draws a hurt and Blake wins the game if he draws s black card. Where, if a player does not win on their turns then card is return to the deck and then deck is shuffled and it becomes the turn of other player, where the game has four states: Heather wins, Blake wins, Heather’s turn and Blake’s turns.

Answer 11

(c)

To determine

To calculate: The stable matrix, if Heather and Blake play a card game in which they take turns drawing a card from a shuffled deck of 52 cards, Heather wins the game if she draws a hurt and Blake wins the game if he draws s black card. Where, if a player does not win on their turns then card is return to the deck and then deck is shuffled and it becomes the turn of other player, where the game has four states: Heather wins, Blake wins, Heather’s turn and Blake’s turns.

Answer 12

(d)

To determine

To calculate: The probability that Heather wins if she got first, if Heather and Blake play a card game in which they take turns drawing a card from a shuffled deck of 52 cards, Heather wins the game if she draws a hurt and Blake wins the game if he draws s black card. Where, if a player does not win on their turns then card is return to the deck and then deck is shuffled and it becomes the turn of other player, where the game has four states: Heather wins, Blake wins, Heather’s turn and Blake’s turns.

Answer 13

(d)

To determine

To calculate: The probability that Heather wins if she got first, if Heather and Blake play a card game in which they take turns drawing a card from a shuffled deck of 52 cards, Heather wins the game if she draws a hurt and Blake wins the game if he draws s black card. Where, if a player does not win on their turns then card is return to the deck and then deck is shuffled and it becomes the turn of other player, where the game has four states: Heather wins, Blake wins, Heather’s turn and Blake’s turns.

Answer 14

(e)

To determine

To calculate: The expected number of turns if heather got first, if Heather and Blake play a card game in which they take turns drawing a card from a shuffled deck of 52 cards, Heather wins the game if she draws a hurt and Blake wins the game if he draws s black card. Where, if a player does not win on their turns then card is return to the deck and then deck is shuffled and it becomes the turn of other player, where the game has four states: Heather wins, Blake wins, Heather’s turn and Blake’s turns.

Answer 15

(e)

To determine

To calculate: The expected number of turns if heather got first, if Heather and Blake play a card game in which they take turns drawing a card from a shuffled deck of 52 cards, Heather wins the game if she draws a hurt and Blake wins the game if he draws s black card. Where, if a player does not win on their turns then card is return to the deck and then deck is shuffled and it becomes the turn of other player, where the game has four states: Heather wins, Blake wins, Heather’s turn and Blake’s turns.

Answer 16

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Answer 19

Ch. 8.1 - 1. Is a stochastic matrix? Ch. 8.1 - 2. Learning Process An elementary learning process...Ch. 8.1 - In Exercises 1-6, determine whether or not the...Ch. 8.1 - In Exercises 1-6, determine whether or not the...Ch. 8.1 - In Exercises 1-6, determine whether or not the...Ch. 8.1 - Prob. 4E Ch. 8.1 - In Exercises 1-6, determine whether or not the...Ch. 8.1 - Prob. 6E Ch. 8.1 - In Exercises 7–12, write a stochastic matrix...Ch. 8.1 - Prob. 8E

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