Question

Objective: This activity has the purpose of helping students apply Markov Chain for transitions probabilities and to calculate expected values from a Markov Chain Process (Objectives 2&3) Student Instructions: 1. For the following exercise calculate the probability in a document 2 Upload and attach your file in PDF format to the Assignment Submission area in Blackboard You may perform your diagram in a piece of paper 3. This assessment is worth 5 points and you have 2 attempts to complete it You will not get the points until you have completed the self-assessment 4. For due date refer to the course Calendar in the Tools area of Blackboard According to Bird lovers, the probability that both bird at stage 1 is 0.80, what would be the probability to see only Dabbling in stage 2? Whistler Dabbling Both Neither 0.70 0.20 0.10 0.10 080 000 0.050.050.10 0.80 0.20 0.05 05 0.60 0.10 0.10 Whistler Dabbling Both Neither

Please step by step.

Answer 1

The given transition matrix is for state 1.

We can see that the transition probability from state "Both" to state "Both" is 0.80. Thus the probability that both bird are at stage 1 is 0.80

For stage 2, the probability to see only Dabbling in stage 2 is the transition probability from state "Dabbling" to state "Dabbling" in stage 2. The transition probability from state "Dabbling" to state "Dabbling" is at row 2 and col 2 of the matrix.

By matrix multiplication method, for stage 2, the transition probability from state "Dabbling" to state "Dabbling" at row 2 and col 2

= Sum of product of all entries from row 2 with corresponding elements of column 2

= P(2, 1) * P(1, 2) + P(2, 2) * P(2, 2) + P(2, 3) * P(3, 2) + P(2, 4) * P(4, 2) (P(r, c) is the probability at row r and column c)

= 0.20 * 0.20 + 0.60 * 0.60 + 0.10 * 0.10 + 0.10 * 0.05

= 0.415