Homework Assignment #2
Due date: before class on Wednesday, 10/5
1. Normal and Lognormal Distributions.
(a) Suppose that the log return, is normally distributed with mean -0.0124 and standard deviation
0.0675, what is the mean and stan
# Donskers Theorem #
n=500 # total number of steps in a random walk
t=0.3 # focus on t=0.3, based on the theorem, W_cfw_n,0.3 should converges to
Wiener process W(0.3)
sim=10000 # simulate 10000 random walk paths
W <- numeric(sim)
for ( i in 1:sim)cfw
Homework Assignment #1
Due date: before class on Friday, 9/16.
All tests are based on the 5% significance level.
R packages quantmod and fBasics are helpful in doing this assignment.
1. Suppose that X Bernoulli(p) with p 2 (0,
1. Stochastic Process.
A stochastic process cfw_Xt is a collection cfw_Xt : t I of random variables where the index t
belongs to the index set I . Typically, I is an interval in R (in which case we say that cfw_Xt
Money borrowing and lending involve interest. Interest rates
ordinary people work with are compounded annually,
semiannually, quarterly, monthly, weekly or daily.
Example: Suppose that $100 is invested for a year with interest rate 10%
# Payoff and profit of a call option from a long position at time of maturity
r <- 0.08 # interest rate
premium <- 3 # premium per share
T <- 0.5 # expiration date
K <- 25 # strike price
payoff <- function(x) sapply(x, function(x) max(c(x - K, 0)
One-step Binomial Tree
Suppose that a stock has price $100/share at current time and its
price at the end of one month will be either $90 (down state) or
$110 (up state). Assume that a call option exists on this stock.
The call option has a strike price o
Association Categorical and Quantitative - Solutions
1: Open the Class Survey (Minitab File) found in the Data Sets folder. Use Stat>Tables>CrossTabulation and Chi-Square to answer the following questions. Put Gender (C2) in the row and the variable Ever
Hypothesis Testing Comparing Two Groups - Solutions
1 For each of the following research questions does the situation or research question involve independent samples or paired data? a. Twenty-five people have their cholesterol measure before eating a Big
Practice Second Midterm
October 16, 2014
There are 22 questions below. There are actually two practice exams below; the odd numbered
questions comprise one exam and the even numbered
questions comprise the other.
2. I performed Fishers Test for a balanced
Practice Midterm Exam
(c) A female and not a veteran.
3. The 1,000 students at a small state university are classied according to two features.
Partial results are in the table below.
1. Alicia will
Solutions to Practice Final,
Statistics 371, Spring, 2014.
(a) Use these data to obtain Gossets 95%
condence interval estimate of the mean
of the unknown pdf.
Answer: The number of degrees of freedom is:
(a) What is Corbins value of k?
Probability Distributions - Solutions
1 In each part, indicate, (1) whether the variable is discrete or continuous AND (2) whether it is
binomial or not AND (3) if it is binomial, give values for n and p.
a. Number of times a head is flipped in 10 flips o
Confidence Intervals Proportion and One Mean - Solutions
1 The term sampling frame refers to the group that actually had a chance to get into the sample. Ideally, this is the same as the population of interest, but sometimes it isn't. In the following sit
Multiple Linear Regression - Solutions
1 Relationship Between Eighth Grade IQ, Eighth Grade Abstract Reasoning and Ninth
grade Math Score For a statistics class project, students examined the relationship between x 1 = 8th
grade IQ, x2 = 8th grade Abstrac
Sampling Distributions Solutions
1 Suppose the amount students at PSU spent on textbooks this semester is a normal random
variable with mean = $360 and standard deviation = $90.
a. Use the empirical rule for bell-shaped data to determine intervals that wi