Practice Exam 1 STAT 1100, Fall 2007 Instructor: Juan Carlos Rodrguez-Raga
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This is a closed-book exam. You are allowed to use a calculator and one two-sided sheet of notes. There are 23 problems, with point values as shown. Parts of problems
Question 2 Fifteen flips of a biased coin are conducted in which the probability of a head is 0.6. Please calculate/provide exact probabilities for each answer. Let X1 = the number of heads in the first ten flips. Let X2 = the number of heads in the last
Functional Widgets Box 1 Box 2 Box 3 Box 4 1900 300 900 900
Defective Widgets 100 200 100 100
Question 7 We have 4 boxes with functional and defective widgets. We select a box i at random, with P (Bi)=1/4 and select a widget from it. What is the probabili
EX IE 111: Tentative Course Schedule, Spring 2009 Note that we will try to stick to this, but things may slip along the way. Thus this must be considered only as a rough guide. Date Topic 1/12 General Introduction 1/14 Sample Spaces and Events 1/16 Interp
Normal Distributions and Approximation to Binomial
Week of March 16 Click to edit Master subtitle style
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Example
Suppose X~N(5,16) a) Find k so that P(X < k) = 0.95 Here we are given a probability, and are asked to find an ordinate. Lets work backwa
Go over HW #2 Test Next Friday, February 6 Homework 3 due Wednesday February 4 Will go over HW #3 that Wednesday
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Example
Workers in a nuclear power plant are classified into three groups based on their exposure to radiation, High, Medium and Low.
IE 111 Spring 2009 Homework #7 Solutions Question 1. Consider the following probability density function (PDF): fX(x) = kx2 fX(x) = 0 for 0 x 1 otherwise
a) Find k so that we have a valid probability density function.
x3 k 1 = k x dx = k = thus k = 3 3 0
Continuous Uniform and Normal Distributions
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Continuous Uniform Dist.
The uniform distribution is probably the simplest continuous distribution. Its distribution in general form is: fX(x) = 1/(b-a
Today
Independence Multiplication and Total Probability rules Finish Independence Go over HW Test on Friday, not Wed.
Friday
Next week
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Conditional Probability
The following is very important:
Definition of Conditional Probability
P( A B) P( A |
IE 111 Spring 2009 Homework #6 Due Wednesday, March 18 Question 1 Suppose you go shopping at a convenience store, pick your items, and then join the line for the cash register. There are 6 people in the line ahead of you, plus one person who is currently
Continuous Random Variables
Week of March 16 Click to edit Master subtitle style
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Intro
Domain defined on set of real numbers
Unlike discrete r.v.s that are finite or countably infinite Domain will be interval: all real numbers between [a,b] Or a ra
Today
Finish counting and multichoose Have read through Chapter 2-4 Conditional probabilities Homework #2 due Read Chapter 2-5 Multiplication and Total Probability rules
Wed.
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Conditional Probability
It is often useful to be able to calculate the
IE 111 Spring 2009 Homework #5 Question 1 Let X be a Binomial random variable with n=100, p=.7 (a) Which one of the following Excel formulas will calculate Pr(X=100) ? =BINOMDIST(0,100,.7,TRUE) =BINOMDIST(100,100,.7,TRUE) =BINOMDIST(0,100,.7,FALSE) =BINOM
The Poisson Distribution
The Poisson Distribution is another extremely important distribution in Probability and Statistics. It is especially important for Industrial Engineers for reasons that will become apparent. The distribution was discovered by Simo
If we flip 10 coins, what is the probability that we get exactly 5 heads? Answer: Suppose we write outcomes as we have in the past. For example HHTTHHTHTT is an example of an outcome with exactly 5 heads. How many total outcomes are there
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If we fl
IE 111: Engineering Probability and Statistics Syllabus: Spring Semester 2009 Course Description This course is an introductory course to the fields of Probability and Statistics designed for engineering students. The course focuses primarily on the study
Example 2
Your birthday is coming up, and you are afraid that your wife might be planning a surprise party for you. In the past she has thrown you a surprise party on 10% of your birthdays. However, you know that if she is going to throw a party, there is
The Poisson Process
The most useful application of the Poisson distribution is in the modeling of purely random processes, also known as Poisson processes. A Poisson Process models an arrival process. For example
the arrival of emergency patients to a hos
Classical Interpretation
Consider experiment with finite S = cfw_s1,s2,sN All outcomes are equally likely to occur
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Axiom 3
Let A be an event defined on S, and let a1 , a2, . , an be the outcomes (elements) comprising event A This is clearly true si
IE 111 Fall 2008 Homework #3 Officially Due on Friday 9/19 Material on this homework will be fair game for the exam on Wed 9/17
1. Learn the concept of conditional probability by Venn diagram a) If P(A|B) =1, must A=B? Draw a Venn diagram to explain your
The Mean and Variance of a Random Variable
Two important quantities that describe the behavior of a random variable and PMF. The mean is also equivalently known as the Expected Value. We can denote the mean/expected value or expectation of a random variab
Axioms of Probability
Axiom 1
0
Axiom 2
P(S) = 1 Axiom 3
Axiom 3 in words. Given that 2 events A and B are M.E., the probability of at least 1 of these events is the sum of their probabilities. Prcfw_AB = Prcfw_A or B
Ei E j = when i j P j Ei = P ( Ei ) i
IE 111 Spring Semester 2009 Homework #2 Due Wednesday, 01.28.09 Question 1 An order for a personal digital assistant can specify any one of five memory sizes, any one of three types of displays, any one of four sizes of a hard disk, and can either include
Example: Acceptance Sampling A common application of the hypergeometric distribution is in "acceptance sampling".
Acceptance sampling occurs when a supplier delivers a Lot (e.g. a truckload full, a box full, or, in general, a bunch of) material (parts, fr
IE 111 Spring Semester 2009 Note Set #1
Introduction
This course will cover the fundamentals of probability theory. It is essentially a mathematics course (indeed the Accreditation Board of Engineering and Technology, which accredits engineering schools,
IE 111 Spring Semester 2009 Homework #1 Due Wednesday 01/21/09
Question 1. Consider the Venn diagram at right with events A, B, C, and D as shown when you answer questions a) through e). a) Give a set representation of the shaded region.
B A D S C
Indicat
Summary Examples
Example 1 An experiment consists of tossing a die and then flipping a coin once if the die outcome is even. If the die outcome is odd, the coin is flipped twice. a) Describe the sample space by listing its elements. b) Describe the sample
I E 111 HW#10 David Gri tz 1. (a) 1 (b) 0/0.5=0 (c) Yes, the area is the same for both shapes showing the joint is the product of the marginals. (d) 0.25/0.5=.5 (e) 1.5/1=1.5 2. (a) F(y) = 4x2 (b) F(y) = 4(x-0.25)2 (c) F(y) = 4(x-0.125)2 3. (a) Marginal (