Reflection and Comparison: Put the table with total interest earned for each year, for each
type of investment, into your project. What is the most beneficial investment for you? Justify
your answer in terms of total interest earned after 25 years. Write
Statistics 355 Homework 1
Problem 2.4
Each of the sample of four home mortgages is classified as fixed rate (F) or variable rate (V).
a. What are the 16 outcomes in S?
FFFF
VFFF
FFFV
VFFV
FFVF
VFVF
FFVV
VFVV
FVFF
VVFF
FVFV
VVFV
FVVF
VVVF
FVVV
VVVV
b. Whic
Statistics 355 Homework 7
Problem 4.1
The current in a certain circuit as measured by an ammeter is a continuous random
variable X with the following density function:
(
0.075x + 0.2, 3 x 5
f (x) =
0
otherwise
0.3
0.0
0.1
0.2
f
0.4
0.5
a. Graph the pdf an
Statistics 355 Homework 3
Problem 2.71
An oil exploration company currently has two active projects, one in Asia and the other
in Europe. Let A = the Asian project is successful and event B = the European project
is successful. Suppose that A and B are in
Statistics 355 Homework 21
Problem 12.9
The flow rate y (m3 /min) in a device used for air-quality measurement depends on the
pressure drop x (in. of water) across the devices filter. Suppose that for x values between
5 and 20, the two variables are relat
Statistics 355 Homework 5
Problem 3.29
The pmf of the amount of memory X (GB) in a purchased flash drive was given in
Example 3.13 as:
x
1
2
4
8
16
p(x) 0.05 0.10 0.35 0.40 0.10
Compute the following:
a. E(X)
x
1
2
4
8
16
p(x) 0.05 0.10 0.35 0.40 0.10
xp(
Statistics 355
1. A box contains six 40-W bulbs, five 60-W bulbs, and four 75-W bulbs.
a. If bulbs are selected one by one in random order, what is the probability that at
least two bulbs must be selected to obtain one that is rated 75 W?
Let A = event th
Statistics 355 Homework 10
Problem 5.1
A service station has both self-service and full-service islands. On each island, these is
a single regular unleaded pump with tow hoses. Let X denote the number of hoses being
used on the self-service island at a pa
Statistics 355 Homework 4
Problem 3.5
If the sample space S is an infinite set, does this necessarily imply that any rv X defined
from S will have an infinite set of possible values? If yes, say why. If no, give an example.
NO. Multiple Responses
Problem
Statistics 355 Homework 17
Problem 9.1
An article in the November 1983 Consumer Reports compared various types of batteries.
The average life-times of Duracell Alkaline AA batteries and Eveready Energizer Alkaline
AA batteries were given as 4.1 hours and
Statistics 355 Homework 11
Problem 5.37
A particular brand of dishwasher soap is sold in three sizes: 25 oz, 40 oz, and 65 oz.
Twenty percent of all purchasers select a 25-oz box, 50% select a 40-oz box, and the
remaining 30% choose a 65-oz box. Let X1 an
Statistics 355
Problem 1
An oil exploration company currently has two active projects, one in Asia and the other
in Europe. Let A = the Asian project is successful and event B = the European project
is successful. Suppose that A and B are independent with
Statistics 355 Homework 22
Problem 12.31
During oil drilling operations, components of the drilling assembly may suffer from sulfide
stress cracking. The article reported on a study in which the composition of a standard
grade of steel was analyzed. The f
Statistics 355 Homework 15
Problem 8.13
The calibration of a scale is to be checked by weighing a 10-kg test specimen 25 times.
Suppose that the results of different weighings are independent of one another and that
the weight on each trial is normally di
Statistics 355 Homework 2
Problem 2.29
As of April 2006, roughly 50 million .com web domain names were registered (e.g. yahoo.com).
a. How many domain names consisting of just two letters in sequence can be formed?
How many domain names of length two are
Statistics 355 Homework 20
Problem 10.11
An experiment to compare the spreading rates of five different brands of yellow interior
latex paint available in a particular area used 4 gallons (J = 4) of each paint. The sample
average spreading rates (ft2 /gal
Statistics 355 Homework 14
Problem 7.29
Determine the t critical value(s) that will capture the desired t-curve area in each of the
following cases:
a. Central area = 0.95, df = 10
2.228
b. Central area = 0.95, df = 20
2.086
c. Central area = 0.99, df = 2
Statistics 355 Homework 8
Problem 4.29
In each case, determine the value of the constant c that makes the probability statement
correct.
a. (c) = 0.9838
c = 2.14
b. not part of HW
c. P (c Z) = 0.121
P (Z c) = P (Z c) = 0.121 c = 1.17 c = 1.17
Problem 4.31
Statistics 355 Homework 18
Problem 9.37
a. Calculate a confidence interval for the population mean difference between indoor and
outdoor concentrations using a confidence interval level of 95%, and interpret the
resulting interval.
s
0.3868
d t/2,n1
=
Statistics 355 Homework 6
Problem 3.69
Each of 12 refrigerators of a certain type has been returned to a distributor because of
an audible, high-pitched, oscillating noise when the refrigerators are running. Suppose
that 7 of these refrigerators have a de
Statistics 355 Homework 9
Problem 4.77
The authors of the article from which the data in Exercise 1.27 was extracted suggested
that a reasonable probability model for drill lifetime was a lognormal distribution with
= 4.5 and = 0.8.
a. What are the mean
Statistics 355 Homework 12
Problem 5.59
Let X1 , X2 and X3 represent the times necessary to perform three successive repair tasks
at a certain service facility. Suppose they are independent, normal random variables
with expected values 1 , 2 and 3 and var
Statistics 355 Homework 13
Problem 7.1
Consider a normal population distribution with the value of known.
a. What is the confidence level for the interval x 2.81/ n?
99.5%
b. What is the confidence level for the interval x 1.44/ n?
85.02%
c. What value of
Statistics 355 Homework 16
Problem 8.29
The true average diameter of ball bearings of a certain type is supposed to be 0.5 in. A
one-sample t test will be carried out to see whether this is the case. What conclusion is
appropriate in each of the following
Statistics 355 Homework 19
Problem 10.1
In an experiment to compare the tensile strengths of I = 5 different types of copper
wire, J = 4 samples of each type were used. The between-samples and within-samples
estimates of 2 were computed as MSTr = 2673.3 a
Financial Mathematics
for Actuaries
Chapter 2
Annuities
Learning Objectives
1. Annuity-immediate and annuity-due
2. Present and future values of annuities
3. Perpetuities and deferred annuities
4. Other accumulation methods
5. Payment periods and compound
Assignment 3, Stat 633
Rabab Elnaiem
September 27, 2015
1
Problem 1:
a. Develop an accept-reject algorithm to generate from the Beta(a, b) distribution (assume a >
1, b > 1). Use U nif orm(0, 1) as the instrumental density, and derive the optimal value of
Homework 3: Stat 433/633, Fall 2015
Due: Monday, September 28, 2015
1. (a) Develop an accept-reject algorithm to generate from the Beta(a, b) distribution (assume
a > 1, b > 1). Use Uniform(0, 1) as the instrumental density, and derive the optimal
value o