Math 3215: Final Exam Sample Questions
Will Perkins
April 26, 2012
1
Basic Probability
1. Write a formula for Pr[A B C ] in terms of probabilities of intersections of events.
2. What is the dierence between an outcome and an event?
3. You roll a single di
2
2. Suppose that the diameter at breast height of a certain type of tree is normally distributed with = 8.8
and = 2.8 (in inches).
(18 points)
(a) What is the probability that the diameter of a randomly selected tree will be at least 11 inches?
(Give a n
ISyE 3770: Statistics & Applications
Week 6:
Midterm I (covers Ch 1-4 of our context)
Time:
10:05-10:55am on
Friday, September 25.
(Closed books. Calculators OK.
2 cheat sheets, double sides OK.)
The solution sets to HW#1-4 are available
at T-square.
Qu
ISyE 3770: Statistics & Applications
Week 10-12: read Ch 9.1, 9.2
Hypothesis Testing (Ch 9-1)
Tests on the mean of a normal distribution when
variance is known(Ch 9-2)
Midterm II:
Time: 10:05-10:55am, Friday, Oct 30
Closed-book, but 4 cheat sheets all
ISyE 3770: Statistics & Applications
Week 03: Discrete Random Variables
Read Ch. 2 & Ch. 3 of our text
TA: Tony Yaacoub
TA office hours: 11-1pm on Tuesdays
ISyE Main #436
TA Email: tyaacoub@gatech.edu
Review of last week
The axioms of probability:
1. P
3770: Statistics & Applications
Read
Ch 4. Continuous random variables
Continuous Random Variable (Ch4)
Probability density function (pdf):
Cumulative distribution function (cdf):
Mean:
Variance:
Standard Deviation
2
Key properties
For the pdf , we
3770: Statistics & Applications
Week 02
Read Ch. 2 of our text
TA: Tony Yaacoub
TA office hours: 11-1pm on Tuesdays
ISyE Main #436
TA Email: tyaacoub@gatech.edu
Review of last week
Basics of Probability Theory (Ch2 of our text)
Random Experiments, e.g.
ISyE 3770: Statistics & Applications
Week 12-13: read Ch 9.1, 9.2, 9.5
Midterm II Grade Summary
Hypothesis Testing (Ch 9-1)
Tests on the mean of a normal distribution when
variance is known(Ch 9-2)
Tests on proportion (Ch 9-5)
Midterm II Grade Summary
ISyE 3770: Statistics & Applications
Week 13: read Ch 9.3, 10.2
Two-sided tests on the mean of a normal
distribution when variance is unknown (Ch 9-3)
Confidence interval and hypothesis testing on
the difference in means of two normal
distributions when
MATH 3215 ‘ - - ‘Houdré '
Test III . _
- Name: g 7 .
Answer all questions; write neatly, show all work for full credit; closed books, no calcu—
lators. The point value for each problem is indicated. Tables are included. THE HONOR
CODE APPLIES TO THIS CLA
MATH 3215 Houdré
Test II \
‘ Name:
Answer all questions; write neatly, show all work for full credit; closed books, no calcula-
tors. The point value for each problem is indicated. THE HONOR CODE APPLIES TO
THIS CLASS Vs
1. In a certain probability class,
1. For a particular instant lottery, the gambler can determine immediately whether or not a purchased
ticked is a winning ticket. Suppose that the probability of a winning ticket is p = 1/10.
(10pts) Let X be the random number of tickets that must be pur
MATH 3215 Houdré
FINAL EXAM E
I ' " Name: M f
Answer all questions; show all work; closed books, no calculators. Tables are included.
THE HONOR CODE APPLIES
‘ Problem Points Score ‘ 1. A, B and C are three events which occur with respective probabiliti
Review 3, Math 3215, Fall 2015
Problem 1. A random sample of size n = 18 is taken from the distribution with pdf f (x) =
1 x/2, 0 x 2.
(a) Find and 2 .
(b) Find P (2/3 X 5/6), approximately.
Problem 2. Let X1 , X2 , X3 , X4 represent the random times in d
Review 1, Math 3215, Fall 2015
Problem 1. In the gambling game craps, a pair of dice is rolled and the outcome of the
experiment is the sum of the points on the up sides of the six-sided dice. The bettor wins on
the first roll if the sum is 7 or 11. The b
HW1
1. (Problem 1-3) Draw one card at random from a standard deck of cards. The sample space
1
S is the collection of the 52 cards. Assume that the probability set function assigns 52 to each of
the 52 outcomes. Let
A = cfw_ x : x is a jack, queen, or kin
HW2
1. (Problem 1.2-1) A boy found a bicycle lock for which the combination was unknown. The
correct combination is a four-digit number, d1 d2 d3 d4 , where di , i = 1, 2, 3, 4 is selected from
1, 2, 3, 4, 5, 6, 7, and 8. How many dierent combinations are
REVIEW GUIDE FOR MIDTERM 1
1. Read the lecture notes.
2. Glance through the chapters 1.1, 1.2, 1.3, 1.4, 1.5, 2.1, 2.2 and 2.3 in the book.
3. Make sure that you know the following notions (and denitions):
Chapter 1.1:
Random experiment
Random outcome
Out
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