CLO $2\mathrm{.}5$ Select, use, and adapt advanced digital technological and ICT tools in solving modeling problems

$[2$Points$]$ Using the LCG defined by $m=32,a=7,c=13,$ and $Z_0=11$ generate all possible random numbers. Does it has a full period? If no$,$ adjust the value of $"$a$"$ and generate the full period random number. Use all available checks.

CLO $3\mathrm{.}1$ Commitment of integrity and professionality when dealing with various modeling problems. CLO $2\mathrm{.}2$ Choose and apply the suitable modeling method.

CLO $2\mathrm{.}3$ Use the appropriate modeling technique based on the problem nature.

$[3$Points$]$

a$)$ Write down all statistical models appropriate to the following application areas:

Queuing systems

Inventory and supply$-$chain systems

Reliability and maintainability

Limited data

b$)$ A computer repair person is "beeped" each time there is a call for service. The number of beeps per hour $$ Poisson $(=2$ per hour$).$ Find:

i$.$ The probability of three beeps in the next hour:

c$)$ A lamp per hour$),$ hence, on average, $1$ failure per $3$ hours.

ii$.$ The probability that the lamp lasts longer than its mean life is:

iii. The probability that the lamp lasts between $2$ to $3$ hours is:

iv$.$ The probability that it lasts for another hour given it is operating for $2\mathrm{.}5$ hours:

CLO $2\mathrm{.}2$ Choose and apply the suitable modeling method.

CLO $2\mathrm{.}3$ Use the appropriate modeling technique based on the problem nature.

CLO $3\mathrm{.}1$ Commitment of integrity and professionality when dealing with various modeling problems.

$[1$Point$]$ Using the Inverse$-$transform Technique and for the given exponential distribution function compute the desired random variety $"x"$ for any random Number $"R"$ where $PDF=f(x)=e^{-x}$ and $CDF=F(x)=1-e^{-x},$ Calculate X for $R=0\mathrm{.}1754$ and $=1$

CLO $2\mathrm{.}1$ Apply different types of models and validate them.

CLO $2\mathrm{.}3$ Use the appropriate modeling technique based on the problem nature.

CLO $3\mathrm{.}1$ Commitment of integrity and professionality when dealing with various modeling problems.

$[1\mathrm{.}5$Point$]$ For the following terminating simulations suggest the event $E$ that specifies the length of each run as well as the initial conditions.

a$)$ A bank opens from $9$ a$.$m$.$ to $5$ p$.$m$.$

b$)$ A Football game between a blue team and a red team

c$)$ An aerospace manufacturer receives a contract to produce $100$ airplanes, which must be delivered within $18$ months. The company would like to simulate various manufacturing configurations to see which one can meet the delivery deadline at least cost.