Quiz-exam template
Forfatter:
vishal
Sidst opdateret:
5 år siden
Licens:
Creative Commons CC BY 4.0
Resumé:
Quiz-exam template
\begin
Opdag hvorfor 18 millioner mennesker verden rundt stoler på Overleaf med deres arbejde.
\begin
Opdag hvorfor 18 millioner mennesker verden rundt stoler på Overleaf med deres arbejde.
\documentclass[letterpaper,12pt,addpoints]{exam}
\usepackage[utf8]{inputenc}
\usepackage[english]{babel}
\usepackage[top=1in, bottom=1in, left=0.75in, right=0.75in]{geometry}
\usepackage{amsmath,amssymb}
\newcommand{\university}{SKIT COLLEGE }
\newcommand{\faculty}{Faculty of Applied Science and Engineering}
\newcommand{\class}{ME-201}
\newcommand{\examnum}{QUIZ \#3}
\newcommand{\content}{Discrete Random Variables \& Probability Distributions}
\newcommand{\examdate}{30 AUGUST 2019}
\newcommand{\timelimit}{50 minutes}
\pagestyle{headandfoot}
\firstpageheader{}{}{}
\firstpagefooter{}{Page \thepage\ of \numpages}{}
\runningheader{\class}{\examnum}{\examdate}
\runningheadrule
\runningfooter{}{Page \thepage\ of \numpages}{}
\begin{document}
\title{\Large \textbf{\university\\ \faculty\\
\bigskip
\class -- \examnum \\ \content}}
\author{Instructor: Prof. CM sir}
\date{\examdate}
\maketitle
\begin{flushleft}
\makebox[12cm]{\textbf{Name}:\ \hrulefill}
\medskip
\makebox[12cm]{\textbf{Roll Number}:\ \hrulefill}
\end{flushleft}
\noindent \rule{\textwidth}{1pt}
\noindent This exam contains \numpages\ pages (including this cover page) and \numquestions\ questions. Total of points is \numpoints.\\
Good luck and Happy reading work!
\begin{center}
\textbf{Distribution of Marks}\\
\medskip
\gradetable[v][questions]
\end{center}
\clearpage
\begin{questions}
\question
In a particular game, a fair die is tossed. If the number of spots showing is either 4 or 5 you win $1, if the number of spots showing is 6 you win $4, and if the number of spots showing is 1, 2, or 3 you win nothing. Let X be the amount that you win.
Which of the following is the expected value of X?
\begin{parts}
\part 1.00
\part 2.50
\part 4.00
\part 6.00
\end{parts}
\clearpage
\question
The weight of written reports produced in a certain department has a Normal distribution with mean 60 g and standard deviation 12 g. The probability that the next report will weigh less than 45 g is
\begin{parts}
\part 0.1056
\part 0.3944
\part 0.1045
\part 0.8944
\end{parts}
\clearpage
\question A small store keeps track of the number X of customers that make a purchase during the first hour that the store is open each day. Based on the records, X has the following probability distribution.
The standard deviation of the number of customers that make a purchase during the first hour that the store is open is
\begin{parts}
\part[4] $P(X=1)$
\part[3] $P(X \geq 4)$
\end{parts}
\clearpage
\question A reservation service employs five information operators who receive requests for information independently of one another, each according to a Poisson process with rate $\mu=2$ per minute.
\begin{parts}
\part[4] What is the probability that during a given 1-min period, the first operator receives no requests?
\part[4] What is the probability that during a given 1-min period, exactly four of the five operators receive no requests?(\textit{Hint}: treat either as a binomial process of 5 trials with 4 successes or consider 5 combinations of Poisson processes, e.g. only 1st operation receives a request or only 2nd operation receives a request and so on)
\end{parts}
\end{questions}
\clearpage
\centering \textbf{\large Probability mass/distribution functions}
\flushleft \textbf{Binomial Distribution}
$$f(x;n,p)=b(x;np)=\binom{n}{x}p^x(1-p)^{n-x}$$
$$\mu=E(x)=np$$
$$\sigma^2_x=np(1-p)$$
\flushleft \textbf{Hypergeometric Distribution}
$$P(X=x)=h(x;n,M,N)=\frac{\binom{M}{x}\binom{N-M}{n-x}}{\binom{N}{n}}$$
$$\mu=E(X)=\frac{nM}{N}$$
$$\sigma^2_x=n\frac{M}{N}\frac{N-M}{N}\frac{N-n}{N-1}$$
\flushleft \textbf{Poisson Distribution}
$$P(x;\mu)=e^{-\mu}\frac{\mu^x}{x!}$$
$$E(X)=Var(X)=\mu$$
\clearpage
This page is intentionally left blank to accommodate work that wouldn't fit elsewhere and/or scratch work.
\end{document}