Question: A server computer is checked at the end of each hour. As a result of the control It can be seen that the server is

A server computer is checked at the end of each hour. As a result of the control

It can be seen that the server is either working or broken. If the check shows that the server is working,

The probability that the server will remain up for the next hour is

0.90 .

If you check that the server is corrupt

If it is detected, the server will be repaired and this repair process may take more than

1

hour. Whenever

If the server is down, regardless of how long the server has been down

The probability that the server is still down after

1

hour is

0.35 .

(

)

Explain why the state of the server at the end of each hour is a Markov chain.

(

)

Write the

1 -

step transition probability matrix of the Markov chain and draw the transition diagram.

(

)

Given that the server is up at time

0,

it will still be up after

3

hours

Find the probability of happening.

(

)

The probability that the server is up and running at time

0

0.7 .

Your server is down after

4

hours

Find the probability of happening.

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