During the process execution, Process $1$ spends the following time units in different five states:

In NEW state $2$ units

In READY state $75$ units

In RUNNING state $130$ units

In WAITING state while exclusively performing I$/$O: $27$ units

IN TERMINATE state: $2$ units.

What are: Turnaround time: Ttr$,$ Waiting time Tw$,$ and Total execution time $($CPU $+$ I$/$O$).$ Show all calculations in the submitted file.

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Processes perform the following operations:

P$1$: input$($a$),$ output$($d$)$

P$2$: calculates b$=$a$*$c

P$3$: input$($c$),$ calculates d$=$a$+$b$+$c

Write the main program and three processes and synchronize them using semaphores.

T$($n$+1)=$ atn $+(1-$a$)$T$($n$)$

derive the formula for T$(2)$ as a function of t$0,$ t$1,$ and T$(0)$

$($b$)$ Calculate T$(2)$ for the given measured sequence of CPU bursts $\{3,7\},$ and for T$(0)=4,$ and for two values of the coefficient a: a$=0\mathrm{.}3($T$(2)\text{'})$ and a$=0\mathrm{.}6[$T$(2)\text{'}\text{'}\}.$