$\{$

"cells": $[$

$\{$

"cell$\_$type": "code",

"execution$\_$count": $7,$

"metadata": $\{\},$

"outputs": $[],$

"source": $[$

$"$

$",$

$"$# your name:

$",$

$"$# your id:$"$

$]$

$\},$

$\{$

"cell$\_$type": "markdown",

"metadata": $\{\},$

"source": $[$

"Part a is $60$ points, Part b is $20,$ Part c and d are $10$ points

$",$

$"$

$",$

"Visitors$$ parking at Ozark College is limited to five spaces only. Cars making use of this space

$",$

"arrive according to a Poisson distribution at the rate of six cars per hour. Parking time is exponentially

$",$

"distributed with a mean of $30$ minutes. Visitors who cannot find an empty space on

$",$

"arrival may temporarily wait inside the lot until a parked car leaves. That temporary space can

$",$

"hold only three cars. Other cars that cannot park or find a temporary waiting space must go

$",$

"elsewhere. Determine the following:

$",$

$"$

$",$

$"($a$)$ The probability, $p$\_$n$$,$ of n cars in the system.

$",$

$"$

$",$

$"($b$)$ The effective arrival rate for cars that actually use the lot.

$",$

$"$

$",$

$"($c$)$ The average number of cars in the lot.

$",$

$"$

$",$

$"($d$)$ The average time a car waits for a parking space inside the lot."

$]$

$\},$

$\{$

"cell$\_$type": "code",

"execution$\_$count": null,

"metadata": $\{\},$

"outputs": $[],$

"source": $[$

$"$#part a$,$ code here $"$

$]$

$\},$

$\{$

"cell$\_$type": "code",

"execution$\_$count": null,

"metadata": $\{\},$

"outputs": $[],$

"source": $[$

$"$#part b$,$ code here"

$]$

$\},$

$\{$

"cell$\_$type": "code",

"execution$\_$count": null,

"metadata": $\{\},$

"outputs": $[],$

"source": $[$

$"$#part c$,$ code here"

$]$

$\},$

$\{$

"cell$\_$type": "code",

"execution$\_$count": null,

"metadata": $\{\},$

"outputs": $[],$

"source": $[$

$"$#part d$,$ code here"

$]$

$\}$

$],$

"metadata": $\{$

"kernelspec": $\{$

"display$\_$name": "base",

"language": "python",

"name": "python$3"$

$\},$

"language$\_$info": $\{$

"codemirror$\_$mode": $\{$

"name": "ipython",

"version": $3$

$\},$

"file$\_$extension": $".$py$",$

"mimetype": "text$/$x$-$python",

"name": "python",

"nbconvert$\_$exporter": "python",

"pygments$\_$lexer": "ipython$3",$

"version": $"3\mathrm{.}9\mathrm{.}12"$

$\}$

$\},$

"nbformat": $4,$

"nbformat$\_$minor": $2$

$\}$