The base CPI of a computer is $1,$ which includes the TLB and cache access time. The clock rate is $2$GHz$.$ The TLB miss rate is $3\%$ and the cache miss rate is $3\%.$ The main memory access time is $45$ nanoseconds. In addition, the page fault rate is $0\mathrm{.}6\%.$ The hard drive transfer rate is $200$ MB$/$s$,$ and the hard drive overhead $($including all the latency other than transfer time$)$ is $0\mathrm{.}018$ milliseconds. The page size is $4096$ bytes and the sector size is $512$ bytes. The probability that all the sectors are contiguous is $0\mathrm{.}4.$ A cache block to be replaced is dirty with $0\mathrm{.}03$ probability, and a page to be replaced is dirty with $0\mathrm{.}05$ probability. Assume there is no write buffer for writing to memory or hard drive. The cache and page table are full initially.

What is the probability of having TLB hit and cache hit?

Assuming TLB hit and cache hit, what is the average CPI?

What is the probability of having TLB hit and cache miss?

Assuming TLB hit and cache miss, what is the average CPI?

Assuming TLB hit, what is the average CPI?

What is the probability of having TLB miss and cache hit?

Assuming TLB miss, cache hit, what is the average CPI?

What is the probability of having TLB miss and cache miss and no page fault?

Assuming TLB miss, cache miss, and no page fault, what is the average CPI?

Assume a page is stored on contiguous sectors$,$ what is the average number of cycles to read$/$write the page from$/$to the hard drive?

Assume a page is stored on random sectors$,$ what is the average number of cycles to read$/$write the page from$/$to the hard drive?

What is the average number of cycles to read$/$write a page from$/$to the hard drive?

What is the probability of having TLB miss and page fault?

Assuming TLB miss and page fault, what is the average CPI?

What is the overall average CPI?

In the answers, round all the probabilities to the fifth decimal place. Round the average CPI to the nearest tenth. All the decimal places must be present even if they are zero. Keep more digits for intermediate results to avoid large accumulated errors. Separate the answers by commas.

These should be your answers:

$0\mathrm{.}94090,1\mathrm{.}0,0\mathrm{.}02910,93\mathrm{.}7,3\mathrm{.}8,0\mathrm{.}02893,91\mathrm{.}0,0\mathrm{.}00089,183\mathrm{.}7,76960\mathrm{.}0,328960\mathrm{.}0,228160\mathrm{.}0,0\mathrm{.}00018,239751\mathrm{.}7,49\mathrm{.}6$

Can you please show calculations