A software system consists of $n=10$ components $c1,c2,$dots, and $c10.$ Component $c1$ starts the execution and $c10$ outputs the result. The system can be represented by a directed graph $G=(V,E).$ Components are the elements in vertex set $V.$ The edge set $E$ will be arbitrarily determined by you based on the following indegree and outdegree for each component. Assume unit tests have been performed and the individual component reliabilities from $R_1$ to $R_{10}$ for $c1$ to $c10$ are $\mathrm{.}97,\mathrm{.}99,1,\mathrm{.}98,1,\mathrm{.}985,\mathrm{.}975,1,\mathrm{.}965,$ and $\mathrm{.}99,$ respectively. For a component, its outdegree edges have an equal opportunity to be visited. All components perform no recursion calls to itself.

Draw your graph $G.(4$ pts$)$

Print your Matlab or Octave program and show the computed system reliability $R.(4$ pts$)$

$R=(-1{)}^{n+1}\frac{|(I-M{)}_{n,1}|}{|I-M|}{R}_n$

$c1$: indeg$(0),$ outdeg$(2)$

$c2$: indeg$(2),$ outdeg$(3)$

$c3$: indeg$(3),$ outdeg$(2)$

$c4$: indeg$(3),$ outdeg$(1)$

$c5$: indeg$(1),$ outdeg$(3)$

$c6$: indeg$(2),$ outdeg$(4)$

$c7$: indeg$(2),$ outdeg$(2)$

$c8$: indeg$(3),$ outdeg$(2)$

$c9$: indeg$(2),$ outdeg$(1)$

$c10$: indeg$(2),$ outdeg$(0)$

Hints for coding in Matlab or Octave:

$\backslash$table$[[$Create an $n**n$ identity matrix I:,$I=$eye$(n)$Suppose an electrical system consists of four components C$1,$ C$2,$ C$3$ and C$4.$ The corresponding probability that each component works is also shown in the following diagram. Assuming that the components fail independently, what is the probability that the system works? Show steps.