Exam 2 : Study Guide
MATH 166:503 Fall 2015
Administrative details
• The exam is on Friday (October 23rd ) in class. Students will sit in their assigned
seats.
• The exam will consist of three parts. Part I will have 5 questions (5 points each) and
2 questions (4 points each) with multiple-choice answers. Each question will have
only one correct answer and students will clearly mark their choice by encircling
the letter signifying that option or as instructed otherwise. Any ambiguous answer
will be considered incorrect. No work will be graded and no partial credit will be
given for this part except for Question 2 and Question 3.
• Part II will have 1 question with 4 sub-parts (2 points each). Each of them will be
True/False questions. Again, ambiguous answers will be considered incorrect and
no partial credit will be awarded for any of these sub-parts.
• Part III will have 7 short answer type questions (total worth of 59 points). All
necessary work will have to be shown for full credit i.e. answers with no supporting
work will not receive full credit. Partial credit may be awarded for correct work
shown. Final answers will need to be clearly put in a box, whenever possible.
• Use of calculators is permitted, provided they have been cleared before the exam.
If you use your calculator for anything beyond an arithmetic calculation on the
workout problems, please list the commands you used and the input you entered.
Partial credit will be given for appropriate work shown on these problems.
• Round your answers to 4 places of decimals, whenever necessary.
• You will be allowed to enter the room beginning at 12:25pm. Have your ID and
a cleared calculator ready to show when you enter the room and before you
take your seat.
• Bring: Writing Utensils, Picture ID, Calculator. All other materials should
be left at the sides or front of the room during the exam. Electronic devices must
be off or silent and out of sight during the exam.
• Students without a picture ID will have to bring a picture ID to my office
and sign a document allowing them to pick up their exam and have the
grade recorded!
• Students are advised to either remove their hats during the exam or turn it backwards, if they absolutely have to wear it.
1
Suggestions for studying
• Read lecture notes with all worked out examples.
• Read examples from the textbook. (Online copy available in Webassign)
• Review Online Homework problems.
• Review problems from the Week-in-review.
http://www.math.tamu.edu/~dmanuel/math166/wir/index.html
• Review problems from the past Week-in-reviews posted on the Course webpage and
eCampus.
• Practice from the suggested homework problems.
http://www.math.tamu.edu/~sdutta/math166/Math166_PracticeProblems.pdf
• Office Hours (week of exam):
Monday 3:00 - 3:45 PM and 5:15 - 6:00 PM
Thursday 1:30 - 3:30 PM and upon request by email.
Summary of topics (* denotes important topics)
1. Section 2.1
• Multiplication Principle (number of ways of doing a sequence of independent
tasks)
• Factorials (! on calc)
• Permutations (nPr on calc) [keyword - arrange and when “order” is important]
• Distinguishable Permutations* of n objects where n1 objects are identical of the
first kind, n2 are identical of the second kind, · · · , nk are identical of the k th kind
n!
is given by
n1 ! n2 ! · · · nk !
2. Section 2.2
• Combinations (nCr on calc) [keywords - select, pick, choose]
3. Section 2.3
• Probability Using Counting Techniques*
n(E)
n(S)
• Probability of Complement* (P (E) = 1 − P (E C ))
4. Section 2.4
• Bernoulli trials* (binompdf() and binomcdf() on calc)
• Probability of “at least”/ “at most”/ “more than”/ “fewer than”/ etc.
2
5. Section 3.1
• Types of Random Variables*
1. finite discrete
2. infinite discrete
3. continuous
and what values can a random variable take.
• Constructing Probability Distribution tables of random variables *
• Reading Probabilities from a Histogram and completing or drawing missing rectangles in a given Histogram.
6. Section 3.2 - 3.3
• Mean/Average of a list of numbers (1-Var Stats L1 on calc to get x̄)
• Expected Value of a Random Variable, X (1-Var Stats L1,L2 on calc to get x̄)
E(X) = x1 p1 + x2 p2 + x3 p3 + · · · + xn pn
- can be thought of as the center of balance of the Histogram.
• Expected Value of a Binomial Distribution* (µ = np)
• Median of a list of numbers/Random Variable (1-Var Stats L1(,L2) on calc)
- middle value (or mean of two middle values) in a set of data arranged in an
increasing or decreasing order.
- can be thought of as the place where the area of the histogram is cut in half.
• Mode of a list of numbers/Random Variable* (the value of the Random Variable
with the tallest rectangle in the histogram or with the highest probability)
- data may have two modes (bimodal) or have no modes at all.
• Std Dev of a list of numbers (1-Var Stats L1 on calc to get σx)
• Std Dev of a Random Variable* (1-Var Stats L1, L2 on calc to get σx)
• Variance (VARS − > Statistics (option 5) − > σx (option 4) − >
2
(square))
• Variance of a Binomial Distribution* (σ 2 = npq)
7. Section 3.4
• Normal curve
a)
b)
c)
d)
The curve is completely determined by µ and σ.
σ determines sharpness (lesser σ) or flatness (higher σ) of curve.
The curve has a peak at x = µ and symmetric about the vertical line, x = µ.
The curve always lies above the x-axis but approaches the x-axis as x extends
infinitely in either direction.
e) The area under the curve and above the x-axis is 1.
• Normal Distribution - Find P (a < X < b) where a and b are known.
(normalcdf() on calc)
• Find the value a, given P (X < a) = k where k is known. (invNorm() on calc)
3