MATH/STAT 418 Section 002 2008/06/26 Exam 1 Sample
Instructions: 1. There are six problems in this exam. The entire exam is worth 100 points and the point distribution is noted next to each problem. 2. Please show all work as detailed a
Lecture 01
Announcements
Class attendance is important for this course
http:/www.stat.psu.edu/~babu/418/
http:/sites.stat.psu.edu/~babu/418/418SpringSy14.html
Lecture 01
1.1 - 1.2
Set Theory, Basic Concepts
Event: A subset of the sample space (technical r
STAT/MATH 418: Intro to Probability and
Stochastic Processes for Engineering
Chapter 2, Yates & Goodman
CHAPTER 2
Discrete Random Variables
1
STAT/MATH 418: Intro to Probability and
Stochastic Processes for Engineering
Chapter 2, Yates & Goodman
2
Random
STAT/MATH 418: Intro to Probability and
Stochastic Processes for Engineering
Chapter 1, Yates & Goodman
CHAPTER 1
Experiments, Models, and Probabilities
1
STAT/MATH 418: Intro to Probability and
Stochastic Processes for Engineering
Chapter 1, Yates & Good
STAT/MATH 418: Intro to Probability and
Stochastic Processes for Engineering
Chapter 3, Yates & Goodman
CHAPTER 3
Continuous Random Variables
1
STAT/MATH 418: Intro to Probability and
Stochastic Processes for Engineering
Chapter 3, Yates & Goodman
2
Recal
STAT/MATH 418: Intro to Probability and
Stochastic Processes for Engineering
Chapter 5, Yates & Goodman
CHAPTER 5
Random Vectors
1
STAT/MATH 418: Intro to Probability and
Stochastic Processes for Engineering
Chapter 5, Yates & Goodman
N random variables
STAT/MATH 418: Intro to Probability and
Stochastic Processes for Engineering
Chapter 10, Yates & Goodman
CHAPTER 10
Stochastic Processes
1
STAT/MATH 418: Intro to Probability and
Stochastic Processes for Engineering
Chapter 10, Yates & Goodman
2
Stochasti
STAT/MATH 418: Intro to Probability and
Stochastic Processes for Engineering
Chapter 6, Yates & Goodman
CHAPTER 6
Sums of Random Variables &
Moment Generating Functions
1
STAT/MATH 418: Intro to Probability and
Stochastic Processes for Engineering
Chapter
STAT/MATH 418: Intro to Probability and
Stochastic Processes for Engineering
Chapter 4, Yates & Goodman
CHAPTER 4
Pairs of Random Variables
1
STAT/MATH 418: Intro to Probability and
Stochastic Processes for Engineering
Chapter 4, Yates & Goodman
2
Joint c
Lecture 13
Desired outcomes from last class
Students will be able to:
understand the memoryless property of Exponential distribution;
give the mean, variance, p.d.f. and c.d.f. of an Erlang r.v.;
give the mean, variance, p.d.f. and c.d.f. of a Gamma r.v.;
Lecture 06
Desired Outcomes from last class
Lecture 06
2.1
Random Variables
state two forms of the Law of Total Probability;
Random variable is a mapping X from S to R.
solve problems using Bayes Theorem.
The support of X is the set cfw_x R : X (s) = x fo
Lecture 15
Desired outcomes from last class
Lecture 15 4.4, 4.5, 4.10
Independent R.V.
Joint PDF, Marginal PDF &
Students will be able to:
derive a marginal PMF from a joint PMF;
Big shift now:
use a joint PMF to check independence;
Discrete Continuous
gi
Lecture 14
Desired outcomes from last class
Lecture 14
Fucntion (CDF)
4.1
Joint Cumulative Distribution
Students will be able to:
derive the mean and variance of a normal random variable;
Joint CDF of X and Y is
compute probabilities using normal tables;
Lecture 09
Announcements
HW# 3 assignment is at
http:/www.stat.psu.edu/~babu/418/
Lecture 09
Desired Outcomes from last class
Students will be able to:
state and use the PMF of a Poisson r.v.;
Late Homework submissions will not be accepted
derive PMF and
Lecture 08
Desired Outcomes from last class
state and use the PMF of a binomial (n, p) r.v.;
state and use the PMF of a Geometric r.v.
Lecture 08
2.3
The Poisson Random Variable
Goal: Counting blips during a xed interval
Whats a blip? (Warning: Nontechnic
Lecture 03
Desired Outcomes from last class
Students will be able to:
Lecture 03
Example: Roll a die and ip a coin. How many outcomes?
1.8
Counting Methods
A permutation of n objects is a reordering of them.
then
choose
2nd
object
then
.
Therefore, there
Lecture 02
Desired Outcomes from last class
Lecture 02
1.3
Probability Axioms
Students will be able to:
identify the sample space of an experiment;
apply set notation to simplify expressions involving events;
apply Venn diagrams to the same.
Toss of a coi
Lecture 04
Desired outcomes from last class
exploit the multiplication principle when outcomes are equally likely;
Lecture 04
recognize n Pr and
situations; know formulas;
Conditional Probability
Denition: For any events A and B with P (B ) > 0,
dene a pe
Lecture 05
Desired outcomes from last class
dene the conditional probability of A given B using a formula;
understand intuitively what P (A | B ) means;
solve conditional probability problems using formulas or Venn
diagrams;
Lecture 05
1.5
Also known as B
Lecture 07
Desired Outcomes from last class
dene countable, discrete, and support;
dene the p.m.f. of a discrete random variable;
evaluate an unknown multiplicative constant in a p.m.f.
Lecture 07
2.2 Probability Mass Function (PMF)
A lake contains 600 sh
STAT/MATH 418: Intro to Probability and
Stochastic Processes for Engineering
Chapter 12, Yates & Goodman
CHAPTER 12
Markov Chains
1
STAT/MATH 418: Intro to Probability and
Stochastic Processes for Engineering
Chapter 12, Yates & Goodman
2
Discrete-time Ma
Chapter 2 Concept Quiz
1. Which of the following are examples of discrete random variables? (Select all that apply.)
a. Number of customers that arrive at a shop
b. Time spent by a customer in a shop
c. Whether or not a customer buys something while at th
Chapter 1 Concept Quiz
1. What is the sample space for each of the following?
a. Drawing one card from a regular 52-deck of cards and reporting the suit.
b. Drawing two balls from an urn numbered 1,4, without replacement.
c. Hitting a baseball and recordi
Chapter 4 Concept Quiz
1. Please rewrite the following in terms of constants, (), and ():
a. , (1, ) = (1)
b.
, (, ) = 1
c.
, (, 3) = 0
d.
, (, ) = 0
2. Which of the following are definitions of independence for two random variables X and Y
(i.e., if a
Chapter 10 Concept Quiz
1. True or false: An i.i.d random sequence is a discrete-time, discrete-value stochastic
process. False. It can be discrete- or continuous-valued.
2. Fill in the blanks for the definition of a Poisson process () of rate :
a. It is
Data Set
Structure, Net Pay Maps
Sand Tops and Net Sand Counts
Well Survey Data TVD,BHP,SITP?
Reservoir Pressure vs Cumulative Production
Reservoir Pressure Data
Core Analysis
Reservoir Total Production Data
Well Production Data
Reservoir Fluid Study Cove
File: Production Data for Total Reservoir and Wells.xls
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