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16 a) Let X, be a Markov Chain with state space 1. 2. 3) with initial probability distribution (1/4.1/2.1/4). If the one-step transition probability matrix is given by 0 1/4 3/4 P=1/3 1/3 1/3 0 1/4 3/4/ Then compute the following probabilities: a) P(X = 1) by P(X = 2 x = 2/X, = 1) b) A raining process is considered as a two state Markov chain. (X), n = 1,23 ...If it rains it is considered to be state I and if it doesn't rain the chain is in state 2. The transition probability matrix NR 06 0.4) of the chain is given as with initial probabilities of states 1 and 2 are given as 0.4 and 0.2 0.8 0.6 respectively. Find (i) the probability that it will rain for three days from today assuming that it is raining today. (ii) the probability that it will rain after third day and (ii) the probability that it will rain in the long run.

16 a) Let X, be a Markov Chain with state space 1. 2. 3) with initial probability distribution (1/4.1/2.1/4). If the one-step transition probability matrix is given by 0 1/4 3/4 P=1/3 1/3 1/3 0 1/4 3/4/ Then compute the following probabilities: a) P(X = 1) by P(X = 2 x = 2/X, = 1) b) A raining process is considered as a two state Markov chain. (X), n = 1,23 ...If it rains it is considered to be state I and if it doesn't rain the chain is in state 2. The transition probability matrix NR 06 0.4) of the chain is given as with initial probabilities of states 1 and 2 are given as 0.4 and 0.2 0.8 0.6 respectively. Find (i) the probability that it will rain for three days from today assuming that it is raining today. (ii) the probability that it will rain after third day and (ii) the probability that it will rain in the long run.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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16 a) Let X, be a Markov Chain with state space 1. 2. 3) with initial probability distribution (1/4.1/2.1/4). If the one-step transition probability matrix is given by 0 1/4 3/4 P=1/3 1/3 1/3 0 1/4 3/4/ Then compute the following probabilities: a) P(X = 1) by P(X = 2 x = 2/X, = 1) b) A raining process is considered as a two state Markov chain. (X), n = 1,23 ...If it rains it is considered to be state I and if it doesn't rain the chain is in state 2. The transition probability matrix NR 06 0.4) of the chain is given as with initial probabilities of states 1 and 2 are given as 0.4 and 0.2 0.8 0.6 respectively. Find (i) the probability that it will rain for three days from today assuming that it is raining today. (ii) the probability that it will rain after third day and (ii) the probability that it will rain in the long run.
Transcribed Image Text:16 a) Let X, be a Markov Chain with state space 1. 2. 3) with initial probability distribution (1/4.1/2.1/4). If the one-step transition probability matrix is given by 0 1/4 3/4 P=1/3 1/3 1/3 0 1/4 3/4/ Then compute the following probabilities: a) P(X = 1) by P(X = 2 x = 2/X, = 1) b) A raining process is considered as a two state Markov chain. (X), n = 1,23 ...If it rains it is considered to be state I and if it doesn't rain the chain is in state 2. The transition probability matrix NR 06 0.4) of the chain is given as with initial probabilities of states 1 and 2 are given as 0.4 and 0.2 0.8 0.6 respectively. Find (i) the probability that it will rain for three days from today assuming that it is raining today. (ii) the probability that it will rain after third day and (ii) the probability that it will rain in the long run.
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