PSTAT 5A
TEST 2
Practice exam
Your Name:
Your TAs Name:
Your Section Time:
INSTRUCTIONS: FOLLOW CAREFULLY
You have 50 minutes to complete this exam.
Anyone found copying another student work will be given an F for the course.
You are not allowed to consul

Your Name:
Your TAs Name:
Your Section Time:
INSTRUCTIONS: FOLLOW CAREFULLY
You have 50 minutes to complete this exam. You should attempt ALL questions. Anyone found copying
another students work, or cheating in any other way, w ill be given an F for the

Extra Practice Problems: Uniform and Normal Distributions
Ex. 1: What is the advantage of using the median instead of the mean (average) for a
measure of central tendency?
Solution: The mean is effected by extreme values (a.k.a. outliers), while the media

UNIVERSITY OF CALIFORNIA, SANTA BARBARA
Department of Statistics and Applied Probability
PSTAT 5A, Spring 2010
Course Information
Lectures M, W, F, 1:00-1:50 PM, at CHEM 1179
Instructor Riccardo GATTO,
Visiting Associate Professor, UCSB, Associate Profess

Probability Basics Review Notes
Basic Probability Definitions:
* P(A or B) = P(A U B) = P(A) + P(B) P(A and B), for any events A and B.
* Events A and B are mutually exclusive if A and B is empty (nothing in common),
which implies that P(A and B) = 0, sin

Practice Test 4 Solutions
QUESTION 1 [Note: See the solutions to Week 9 Other Problems example that I
emailed for a related type of problem.]
For each day of a business week in June, a local Ice Cream shop recorded the number of
servings of ice cream sold

Practice Test 2 Solutions (from Prof. Gattos website)
Note: Final answers are underlined.
QUESTION 1.
Suppose the test scores of the students at a given test are normally distributed with an expected value of 76
and
standard deviation of 8. What proportio

Practice Test 2 Solutions (from Prof. Gattos website)
Note: Final answers are underlined.
QUESTION 1.
Suppose the test scores of the students at a given test are normally distributed with an expected value of 76
and
standard deviation of 8. What proportio

Practice Test 2 Solutions (from Prof. Gattos website)
Note: Final answers are underlined.
QUESTION 1.
Suppose the test scores of the students at a given test are normally distributed with an expected value of 76
and
standard deviation of 8. What proportio

Practice Test 3 Solutions
QUESTION 1.
A cereal company claims the mean sodium content in one box of its cereal is no more than 230 mg. You
work for a national health service and are asked to test this claim, which is the null hypothesis, against the
alter

Supplementary Problems for Week 10
2. Somebody is interested in studying the relationship between height and weight. Specifically, they
65
60
45
50
55
w e i gh t
70
75
80
are interested in investigating how weight depends on height [thus, weight is the re

LAB Worksheet: Week 5
1. Go to http:/www.shodor.org/interactivate/activities/measures/. Enter in the following: Species Name = plant,
Characteristic = mass, Units of Measurement = grams. For 8 measurements with a range of 0 to 1000 grams, we
will look at

LAB Worksheet: Week 4
1. The time spent waiting in line for concert tickets varies between 1 and 7 hours according to a uniform
distribution. On the website http:/www.socr.ucla.edu/ go to DISTRIBUTIONS CONTINUOUS
UNIFORM DISTRIBUTION. Adjust the parameter

LAB Worksheet: Week 3
1. Consider the experiment where you flip a fair coin 4 times and you are interested in the number of heads that
appear. From the website http:/www.socr.ucla.edu/ go to DISTRIBUTIONS [SOCR DISTRIBUTIONS]
BINOMIAL DISTRIBUTION. Selec

LAB Worksheet: Week 2
1. Look at the Venn diagram at: http:/www.stat.tamu.edu/~west/applets/Venn1.html and read the instructions. The
selected event in the first column ( e.g., A) is shaded in the plot. The probabilities corresponding to each of the event

Extra Notes
Confidence Intervals:
Interpretting them:
We can be [percent] confident that the [population mean / population proportion, but
both must be worded in context of the problem] lies between [lower limit of confidence
interval] and [upper limit of

PSTAT 5A: CLASSROOM SECTION
WEEK 5
SAMPLE DATA
Exercises should be completed during section. When you have finished,
hand in your solutions to your TA for grading. Make sure you show your
work clearly. You may work by yourself or in a group.
1. Suppose th

PSTAT 5A: CLASSROOM SECTION
WEEK 4
UNIFORM AND NORMAL DISTRIBUTIONS
Exercises should be completed during section. When you have finished,
hand in your solutions to your TA for grading. Make sure you show your
work clearly. You may work by yourself or in a

PSTAT 5A: CLASSROOM SECTION
WEEK 3
BINOMIAL DISTRIBUTION
Exercises should be completed during section. When you have finished,
hand in your solutions to your TA for grading. Make sure you show your
work clearly. You may work by yourself or in a group.
1.

PSTAT 5A: CLASSROOM SECTION
WEEK 2
PROBABILITY
Exercises should be completed during section. When you have finished,
hand in your solutions to your TA for grading. Make sure you show your
work clearly and neatly, or no credit may be given.
In the followin

There are 16 different samples and 7 different means.
16 samples
16
PDF of the die value
(population PDF)
7 different means
.3
.2
.1
.0
PDF of sample mean
(sampling PDF)
P(X)
X
1
2
3
4
.3
.2
.1
.0
P(X)
X
1 1.5 2 2.5 3 3.5 4
X = = 2.5
!
!X =
= 0.791
2
=

Division of ordered data into:
halves, gives the median;
quarters, gives the quartiles;
hundreds, gives the percentiles or quantiles
Example. n odd
Sample: 7, 23, 75, 82, 34, 91, 10
2.
The upper (third) and lower (first) quartiles are the
middle observati

There are two types of problems:
Percentiles or quantiles
Definition
Let 0 ! p ! 1, then the pth percentile or
quantile of X, or of the distribution of X, is
the value x such that P( X ! x ) = p.
Note. By distribution of X we mean any function
showing how

Example. We want to compute P( Z ! a )
P( Z ! a ) = 1 P( Z < a)
= 1 P( Z " a)
= 1 F( a )
NORMAL DISTRIBUTION
Continuation
a
0
1
Some approximate probabilities of the
standard normal random variable
P( -1 < Z < 1) = 0.68
P(-2 < Z < 2) = 0.95
P(-3 < Z <

Discrete and continuous random variables
Continuous random variables
A random variable is discrete if we can list or count
all its possible values.
A random variable is continuous if its possible values
cannot be counted.
A continuous random variable can

Example 1
Assume P(A) = 0.2, P(B) = 0.4, P( A " B) = 0.1
Find.P ( AC " B)
More practice examples
P(B ! A ) = P(B )" P(B ! A)
c
!
= 0.4 ! 0.1 = 0.3
Example 3
Example 2
Suppose P(A) = 0.2, P(B) = 0.4, P( A " B) = 0.1
(
Find.P ( A c " B)
Suppose P(A) = 0.2,

EXAMPLES OF INDEPENDENT EVENTS
& 1 #& 1 #
P ( cfw_( H ,5) ) = $ !$ !
% 2 "% 6 "
1. Landing on heads after flipping a coin
1
AND then rolling a 5 on a die (6-sides).
=
12
2. Observe a card with denomination 3, replace
card, reshuffle, AND then observe an a

DEFINITION: independence
Week 2
Probability and Discrete
Random Variables
Two events are independent if the occurrence of one of
the events does not affect the probability of the
occurrence of the other event.
A and B are independent if
P(A I B ) = P(A)P(

EXAMPLE: TREE DIAGRAM
An experiment consists of rolling a six-sided die twice .
Describe the sample space.
1
WEEK 1
WEDNESDAY
2
1
PROBABILITY
2
3
4
The sample space
consists of 36 possible
outcomes.
5
6
1
ANOTHER WAY TO DESCRIBE THE SAMPLE SPACE
1
2
3
4
5