Problem 7. For this Problem use Markor Chains. Two engines are checked daily for
ID: 3305132 • Letter: P
Question
Problem 7. For this Problem use Markor Chains. Two engines are checked daily for possible damages. Probability that the engine is damaged is 0.1. This expeiments ends when both engines are damaged. Part 1. Create Markov diagram to descabe the process. Create the transitional mati Part 2 The 9à power and the 10 power of the transition matx are given below. What is the probability that both engines would die before the tenth year? @What is the psobabilty that both engines would be dead esactly in tenth yeas? Input: Input 0.81 0 09 0.18 0.9 0 0.01 0.1 1 0.81 0 01 0.18 0.9 0 0.01 0.1 1 Result Result 0.150095 0 0 0.474652 0.38742 0. 0.375254 0.61258 1 0.121577 0. 0 0.454204 0.348678 0. 0.42422 0.651322 1.Explanation / Answer
there are two engines
X- number of engine which are damaged
probability of damage = 0.1
probability of no damage = 1-0.1 = 0.9
if X = 0 initially
then X =0 is next step
= (1 -0.1)*(1-0.1) = 0.81
X = 1 is
0.1 *(1-0.1) + (1-0.1)*0.1 = 0.18
X = 2 is
0.1*0.1 = 0.01
b) when X =1 initially
then
P(X =0) = 0 as there is already one damaged , it can't be repaired.
P(X =1 ) = 0.9 {other machine should not get damaged}
P(X =2) = 0.1 { probability of other machine getting damaged}
c)
if X = 2 iniitally
P(X= 0 ) = 0
P(X =1) = 0
P(x =2) = 1
hence the matrix is
P = [0.81 0 0 ; 0.18 0.9 0 ; 0.01 0.1 1];