Course: High Performance Computer Architecture $**$Question: The initial component has an availability of $90\%$ with a Mean Time Between Failure $($MTBF$)$ of $200$ days. To meet higher reliability standards $(95\%$ availability$),$ the organization improved the component but, as a tradeoff, increased the Mean Time To Repair $($MTTR$)$ by $5$ days. What is the new MTBF for the enhanced software?

Assume MTBF $=$ MTTF $+$ MTTR$.$