Write answers to the following briefly.

$($i$)$ If there are $3$ nodes with identical services in a cluster each with availability of $92\%,$ what will be the cluster availability if N$+1$ redundancy model is followed?

$($ii$)$ We need to find the maximum number in a list of $10000$ numbers. How is the list distributed among $10$ MPI processes? How is the maximum number found? Mention which MPI APIs you use for this? Explain. No need to write any code.

$($iii$)$ Compute the number of concurrent users supported by a cluster with $4$ nodes each with $16$ cores, processing time per request is $10$ milliseconds and think time as $1$ minute.

$($iv$)$ We need to transfer a file of $512$ GB to $1000$ clients. Server has $10$Gbps bandwidth. Out of the two methods, Client$-$server and Bittorent, for bulk data transfer, which is faster? Show calculations.