Markov Chains Question involving Probability please help A h

Markov Chains Question involving Probability, please help!

A hard drive in a data center lasts k periods before failing with probability alpha_k, for k = 1, 2, ... Let X_t be the remaining life of the hard drive in service at the end of period t. Thus, X_t = 0 means that X_t + 1 will be the total operating lifetime of the next hard drive installed. Is {X_t} a Markov chain? Explain your answer. If it is a Markov chain, give the transition probabilities; if it is not, give an example where the Markov property is violated.

Solution

No, Xt is not a Markov chain

because it does not have the properties and conditions that a Markov chain have

for example when Xt is the remaining life of .... at the end of period t

that means that the Xt is only at the ond of period t

for that reason Xt is no t a markov chain