In Problems 21-26, use the transition matrix
to find
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- Ff.253.arrow_forwardCan someone please help me with these two questions. I am having so much trouble.arrow_forwardSuppose a two-state experiment has the following transition matrix: 0.5 0.5 1 Answer the following questions: 1. If the experiment is in state 1 on the first observation, what is the probability it will be in state 2 on the second observation? 2. If the experiment is in state 1 on the first observation, what is the probability it will be in state 2 on the fourth observation? ... 3. If the experiment is in state 2 on the third observation, what is the probability that it will be in state 2 on the seventh observation? 4. If the experiment is in state 1 on the third observation, what is the probability it will be in state 1 on the fourth, fifth, and sixth observation?arrow_forward
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- c. The market share of two companies A and B is 30% and 70% in the current time period. The information obtained in terms of the customer loss and retention is given by the matrix P. [0.3 0.2] P = Lo.7 0.8] i.Determine the transition probability matrix in the 1st and 2nd month. ii.What is the steady state of the two companies?arrow_forwardLet us have the experience of a mouse falling into a trap inside a 6-room building, as shown in the figure below. If the room contains k doors, the probability that the mouse will choose one of these doors is 1/k if the mouse reaches room F that contains the food or room S that contains the trap. It will stay there and the experiment ends, the transition matrix is M= [0.5 0 0.5 0 0.3 0 0 ¹0.5 0 0 0.3 0.3 0 0.3 0.3 0 0.5 0 000 O a O b О с 2 000 0.5 0 0.5 0 0 0 0 0.3 0 0.5 0 0.5 M = - 0 0.5 0.5 b 3 ..+. 4 5 0 0 S M= 0 0 0 1 0 0.5 0 0 0 0 0.5 0 0 0.3 0.3 0 0 0.3 0 0.5 0 0 0.5 0 0 1 00000 10 0 000 0.5 0 0 0.5 0 0.3 0 0.3 0.3 0 0.3 0.3 0 0 0 0.5 0 0 000 0 0 0 0 C 0 0 0.3 0.5 1 (a)arrow_forwardthe last 3arrow_forward
- Suppose you have the following transition probabilities. P = Product A B C A 0.40 0 0.60 B 0.30 0.35 0.35 C 0 0.50 0.50 a. Calculate the 3-step transition matrix and interpret each elements.arrow_forwardThe weather in the Magical Land of Oz only depends on the weather from the previous day. There are four possible weather patters: Sunny, Raining, Foggy, and Hailing. The probability transition matrix is given 1: below. S R F H S 1 R 1/2 1/4 1/4 F 1/4 3/4 H 0 0 1/4 3/4 1. If it is Raining today, what is the weather forecast for tomorrow? 2. If it is Raining today, what is the weather forecast for a week from today? 3. If it is Raining today, what is the weather forecast for a year from today? 4. If it is Raining today, what is the weather forecast for ten years from today? 5. Find the stable state vector.arrow_forwardThe following data consists of a matrix of transition probabilities (P) of three competing companies, the initial market share state ℼ(1), and the equilibrium probability states. Assume that each state represents a firm (Company 1, Company 2, and Company 3, respectively) and the transition probabilities represent changes from one month to the next. The market share of Company 3 after three periods is a. 0.259 b. 0.261 c. 0.283 d. 0.296arrow_forward
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