PSTAT 109: Midterm 1 Solutions
Fall 2014
Circle the correct answer for questions 1-6. Each multiple choice question has exactly 1 correct answer.
There is no partial credit awarded for these problems.
PSTAT 109: Lab 5
(Was incorrectly labeled Lab 4 during lab session)
Winter 2014
Instructions: When you nish all problems, ask your TA to check your work.
Problem 1. Let X N ( = 10,
= 3). Using a Z tab
PSTAT 109: Introduction to Excel
Fall 2014
Introduction
In this course, we will at times use Microsoft Excel to aid our statistical analyses. This reference document
focuses on two particular aspects
PSTAT 109: Sample Final Solutions
Fall 2014
(5)
1. Let P be a probability and let A and B be two independent events. Then:
(a) P (AC B) = [1 P (A)]P (B)
(b) P (A B C ) = P (A) + P (B C )
(c) P (AC B)
1. (20 points) There is a continuous random variable X with cumulative distribution function:
x < 0,
0
3
F (x) = 23 (x2 x3 ) if 0 x < 1,
1
x 1.
(a) (4 points) Compute P(0.23 < X < 0.71).
3
F(0.71) - F
Homework #2 - Pstat 109
0.1
Probability and events
2
1. Let ( ; A; P ) a probability space and x A; B 2 A such that P (A) = 7 ,
11
1
C
C
P (B) = 3 and P (A \ B ) = 21 . Compute the following probabili
Instructions: state any formulas that you use before plugging in values. Deﬁne
your events/random variables. The midterm has Spages and is scored out of 100 .
points.
(5) 2. In a survey of 100 UCSB
Summary for Final
PSTAT 109
()
PSTAT 109
1/7
Topics
Operation with sets
Complement
Intersection
Union
Disjoint sets
Rule of Total Probability
De Morgan laws
s
Probability:
Denition in terms of propert
PSTAT 109: Midterm 1 Practice with Solutions
Fall 2014
Circle the correct answer for questions 1-6. Each multiple choice question has exactly 1 correct answer.
There is no partial credit awarded for t
Homework #1 - 2014 - Pstat 109
1. Exercises: page 103-105 # 3.3, 3.4, 3.11, 3.13, 3.14.
2. Prove the De Morgans law:
(A [ B)C = Ac \ B C :
3. Let P be a Probability.
(a) Prove:
P (BnA) = P (B) $ P (A)
PSTAT 109: Quiz 6
Winter 2014
Instructions: Please show all formulas and calculations in an organized fashion
for full credit.
Problem 1. In July 2001, 45% of Americans believed the country was in a r
PSTAT 109: Sample Midterm 2 Solutions
Fall 2014
Circle the correct answer for questions 1-6. Each multiple choice question has exactly 1 correct answer.
There is no partial credit awarded for these pr
PSTAT 109: Midterm 1 Practice
Fall 2014
Circle the correct answer for questions 1-6. Each multiple choice question has exactly 1 correct answer.
There is no partial credit awarded for these problems.
PSTAT 109: Quiz 8
Winter 2014
Instructions: Please show all formulas and calculations in an organized fashion
for full credit.
Problem 1. Suppose a marine biologist was studying a population of lobste
What does 95% mean?
Effect of confidence level and sample size
Determining necessary sample size
We created a (1 )100% confidence interval
for with the formula
( n 1) s
X t / 2
n
As the confidence l
Summary for Midterm
PSTAT 109
()
Summary for Midterm
PSTAT 109
1/3
Topics
Operation with sets
Complement
Intersection
Union
Disjoint sets
Rule of Total Probability
De Morgan laws
s
Probability:
Deniti
PSTAT 109: Quiz 3
Winter 2014
Instructions: Please show all work in an organized fashion for full credit.
Problem 1. Let = cfw_1, 2, 3, and consider the family of subsets A of :
A = cfw_;, , cfw_1, 2,
We created a (1 )100% confidence interval
for with the formula
( n 1) s
X t / 2
n
As the confidence level increases (e.g., 95% to
98%), the interval gets wider
Contains more possible values
In a sa
CLT for population proportion
CI for population proportion
Determining necessary sample size
Survey I: Is Your Hair Black?
A=yes/ B=no
Survey II: Do you own a surfboard? A=yes/B=no
Suppose a fraction
Concept of an estimator
Definition of an unbiased estimator
Computing bias
Efficiency
Comparing unbiased estimators via efficiency
Mean squared error
Collect information: X_1=x_1, X_=x_2,
Want to
Talking about Evidence
Type I and Type II Errors
Two-Sample Inference:
Matched Samples
Independent Samples
Hypothesis tests is a formal way to discuss the weight
of evidence: data vs original claim
Null and alternative hypotheses
Setting a significance level
Test for a population mean: p-values
Rejection regions and connection to CI
We are not sure if a given coin is fair or not: it
may have He
Idea of a confidence interval
CLT
t distribution
Degrees of freedom
Derive CI for
Margin of error
So far, we have used X as an estimate for
is called a point estimate because it gives
a single va
Types of Hypotheses
Test statistic and p-value
Examples: one-sided and two-sided tests
Type I and Type II Errors
Make a claim/ assumption/ hypothesis about
the population you are interested in
Design
Data summary - recap
Boxplots
Sample correlation
Understanding correlation
Aims of Statistical Analysis:
Summarize Data
Visualize Data
Predict (assign probabilities to events)
Quantify evidence t
PSTAT 109: Quiz 1
Winter 2014
Instructions: Please show all work in an organized fashion for full credit.
Problem 1. Check if the following functions are density functions:
(a) f (x) = x 1[0,1] (x)
(b
PSTAT 109: Quiz 4
Winter 2014
Instructions: Please show all formulas and calculations in an organized fashion
for full credit.
Problem 1. Let = [0, 1], and let P be given by P ([a, b]) = b
X to be
X=
PSTAT 109: Quiz 2
Winter 2014
Instructions: Please show all work in an organized fashion for full credit.
Problem 1. Find C1 [ C2 and C1 \ C2 if
(a) C1 = cfw_0, 1, 2, C2 = cfw_2, 3, 4;
(b) C1 = cfw_x
The Quantitative Finance and Investment Track
A guide to Fellowship
The Quantitative Finance and Investment (QFI) track is
intended for actuaries who desire to work with investments.
The investment ac
The Corporate Finance and ERM Track
A guide to Fellowship
The Corporate Finance and Enterprise Risk Management (CFE)
track was borne out of a vision to create a body of study to prepare
actuaries to w