A particular area in a town suffers a high burglary rate. A
sample of 100 streets is taken,
and in each of the sampled streets, a sample of six similar houses
is taken. The table below
shows the number of sampled houses, which have had burglaries
during the last six months.
| No. of houses burgled x | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
| No. of streets f | 39 | 38 | 18 | 4 | 0 | 1 | 0 |
(i) (a) State any assumptions needed to justify the use of a
binomial model for the number of
houses per street which have been burgled during the last six
months.
(b) Derive the maximum likelihood estimator of X bar, the
probability that a house of the
type sampled has been burgled during the last six months.
(c) Determine the probabilities for the binomial model using your
estimate of X bar, and,
without doing a formal test, comment on the fit.
(ii) An insurance company works on the basis that the
probability of a house being burgled
over a six-month period is 0.18. Carry out a test to investigate
whether the binomial
model with this value of p provides a good fit for the data.
NOTE:THERE WAS A MISTAKE ON (b) IT IS ESTIMATOR OF X BAR NOT ESTIMATOR OF P but i have corrected it
In: Statistics and Probability
A report in 2002 found that 21.1% of American adults smoked cigarettes. The town of San Sebastian spent five years focusing on educating their population on the health risks associated with smoking cigarettes, and at the conclusion of this five-year campaign, a study of 1200 participants found that 17.1% of the respondents were current smokers. Is this evidence enough that the public-health campaign has lowered the proportion of smokers in San Sebastian? Use α = 0.02 (Show all steps please)
a)State the null and alternative hypothesis (H0 and Ha). H0: Ha:
b) What is the test statistic for this sample (use at least 3 decimal places)?
c) What is the p-value for this sample? (use Statcrunch)
d)Evaluate the strength of the evidence and state the conclusion (in the context of this question).
In: Statistics and Probability
King Solomon- The Rich Farmer King Solomon is a rich farmer in Tetebia, a town in the Asou Municipal Assembly. He owns over 100,000 hectares of farmlands. However, he fears the worst might happen and wants to do some investments to secure his future and that of his children. He is contemplating several long term investments he could undertake to secure his future and that if his children. He is now 50 years old and he plans to retire in 10 years from active farm work. He expects to live for another 25 years after he retires –that is, until age 85. He heard about an investment in the financial market will help him plan his retirement well. He has no idea about financial markets and how they operate. You recently graduated and have just reported to work as an investment advisor at the brokerage firm of Cenden Ltd. King Solomon has approached your company for advice. Your boss after a discussion with King Solomon could gather the following information. King Solomon wants his first retirement payment to have the same purchasing power at the time he retires as GHȼ 40,000 has today. He wants all of his subsequent retirement payments to be equal to his first retirement payment. (Do not let the retirement payments grow with inflation: King Solomon realizes that the real value of his retirement income will decline year by year after he retires.) His retirement income will begin the day he retires, 10 years from today, and he will then receive 24 additional annual payments. Inflation is expected to be 5% per year from today forward. He currently has GHȼ 100,000 saved up, and he expects to earn a return on his savings of 8% per year with annual compounding. Again, he wants to have a secure university education for his lovely daughter Daisy. His daughter is now 13 years old. She plans to enroll at the University of Professional Studies, Accra in 5 years, and it should take her 4 years to complete her education. Currently, the cost per year (for everything – her food, clothing, tuition, books, transportation, and so forth) is GH¢ 12,000 per year. This cost is expected to remain constant throughout the four-year university education. The daughter recently received GH¢ 7,500 from her grandfather‟s (King David‟s) estate; this money will be invested at a rate of 8% to help meet the costs of Daisy‟s education. The rest of the costs will be met by money King Solomon will deposit in a savings account which also earns 8 percent compound interest per year. He will make 5 equal deposits into the account, one deposit per annum starting one year from now until his daughter starts university. These deposits will begin one year from now. (Assume that school fees are paid at the beginning of the year). Your firm also serves as the investment adviser for Zenzo Pharma Ltd which intends to issue bonds to finance the production of its new vaccine. The bond has a face value of GH¢10,000 at a coupon rate of 12% and a term to maturity of 10 years. The bond expects to pay coupons semi-annually. Your firm however insists on Zenzo Pharma including a call and a sinking fund provision in the bond indenture. The required rate of return on the market for bonds with similar features is 18% per annum. EXAMINER: ISAAC OFOEDA Page 5 Required b. To the nearest cedi, how much must he save during each of the next 10 years (with equal deposits being made at the end of each year, beginning a year from today) to meet his retirement goal? (Note: Neither the amount he saves nor the amount he withdraws upon retirement is a growing annuity.) c. What will be the present value of the cost of 4 years of education at the time the daughter Daisy turns 18? d. What will be the value of the GH¢ 7,500 that Daisy received from her grandfather‟s estate when she starts college at age 18? e. If King Solomon is planning to make the first of 5 deposits one year from now, how large must each deposit be for him to able to put his daughter through college? f. Explain to King Solomon what call provisions and sinking fund provisions are and how these provisions are expected to affect the risk of the bond g. Which value will you place on a bond of Zenzo Pharma Ltd?
In: Finance
King Solomon is a rich farmer in Tetebia, a town in
the Asou Municipal Assembly. He owns over 100,000 hectares of
farmlands. However, he fears the worst might happen and wants to do
some investments to secure his future and that of his children. He
is contemplating several long term investments he could undertake
to secure his future and that if his children. He is now 50 years
old and he plans to retire in 10 years from active farm work. He
expects to live for another 25 years after he retires –that is,
until age 85. He heard about an investment in the financial market
will help him plan his retirement well. He has no idea about
financial markets and how they operate. You recently graduated and
have just reported to work as an investment advisor at the
brokerage firm of Cenden Ltd. King Solomon has approached your
company for advice. Your boss after a discussion with King Solomon
could gather the following information. King Solomon wants his
first retirement payment to have the same purchasing power at the
time he retires as GHȼ 40,000 has today. He wants all of his
subsequent retirement payments to be equal to his first retirement
payment. (Do not let the retirement payments grow with inflation:
King Solomon realizes that the real value of his retirement income
will decline year by year after he retires.) His retirement income
will begin the day he retires, 10 years from today, and he will
then receive 24 additional annual payments. Inflation is expected
to be 5% per year from today forward. He currently has GHȼ 100,000
saved up, and he expects to earn a return on his savings of 8% per
year with annual compounding.
Again, he wants to have a secure university education for his
lovely daughter Daisy. His daughter is now 13 years old. She plans
to enroll at the University of Professional Studies, Accra in 5
years, and it should take her 4 years to complete her education.
Currently, the cost per year (for everything – her food, clothing,
tuition, books, transportation, and so forth) is GH¢ 12,000 per
year. This cost is expected to remain constant throughout the
four-year university education.
The daughter recently received GH¢ 7,500 from her grandfather‟s
(King David‟s) estate; this money will be invested at a rate of 8%
to help meet the costs of Daisy‟s education. The rest of the costs
will be met by money King Solomon will deposit in a savings account
which also earns 8 percent compound interest per year. He will make
5 equal deposits into the account, one deposit per annum starting
one year from now until his daughter starts university. These
deposits will begin one year from now. (Assume that school fees are
paid at the beginning of the year).
Your firm also serves as the investment adviser for Zenzo Pharma
Ltd which intends to issue bonds to finance the production of its
new vaccine. The bond has a face value of GH¢10,000 at a coupon
rate of 12% and a term to maturity of 10 years. The bond expects to
pay coupons semiannually. Your firm however insists on Zenzo Pharma
including a call and a sinking fund provision in the bond
indenture. The required rate of return on the market for bonds with
similar features is 18% per annum.
Required
a)Explain to King Solomon what financial markets mean and which
three (3) financial
instruments he can invest
in.
b)To the nearest cedi, how much must he save during
each of the next 10 years (with equal deposits being made at the
end of each year, beginning a year from today) to meet his
retirement goal? (Note: Neither the amount he saves nor the amount
he withdraws upon
retirement is a growing
annuity.)
c)What will be the present value of the cost of 4
years of education at the time the daughter
Daisy turns
18?
d)What will be the value of the GH¢ 7,500 that Daisy
received from her grandfather‟s estate
when she starts college at age
18?
e)If King Solomon is planning to make the first of 5 deposits one year from now, how large must each deposit be for him to able to put his daughter through college?
f)Explain to King Solomon what call provisions and sinking fund provisions are and how these provisions are expected to affect the risk of the bond
g)Which value will you place on a bond of Zenzo Pharma
Ltd?
In: Finance
Simon Layman is a trust investment officer at a bank in a small affluent town. He enjoys lunching every day with friends at the country club, where his clients have observed him having numerous drinks. Back at work after lunch, he clearly becomes somewhat intoxicated because of his drinking habits and has affected his investment decision-making. His colleagues make a point that Simon handles business with his client in the morning because they distrust his judgment after lunch.
Required:
Based on the above scenario, discuss on Simon’s professional
conduct and the impact on his employer and investment industry in
general by applying the CFA Standards of Practice Handbook. ( 10
marks )
In: Finance
In: Economics
King Solomon is a rich farmer in Tetebia, a town in
the Asou Municipal Assembly. He owns over 100,000 hectares of
farmlands. However, he fears the worst might happen and wants to do
some investments to secure his future and that of his children. He
is contemplating some long term investments he could undertake to
secure his future and that if his children. He is now 50 years old
and he plans to retire in 10 years from active farm work. He
expects to live for another 25 years after he retires –that is,
until age 85. He was advised by a friend that an investment in the
financial market will help him plan his retirement well. He has no
idea about financial markets and how they operate. You recently
graduated and have just reported to work as an investment advisor
at the brokerage firm of Cenden Ltd. King Solomon has approached
your company for advice. Your boss after a discussion with King
Solomon could gather the following information. King Solomon wants
his first retirement payment to have the same purchasing power at
the time he retires as GHȼ 40,000 has today. He wants all of his
subsequent retirement payments to be equal to his first retirement
payment. (Do not let the retirement payments grow with inflation:
King Solomon realizes that the real value of his retirement income
will decline year by year after he retires.) His retirement income
will begin the day he retires, 10 years from today, and he will
then receive 24 additional annual payments. Inflation is expected
to be 5% per year from today forward. He currently has GHȼ 100,000
saved up, and he expects to earn a return on his savings of 8% per
year with annual compounding.
Again, he wants to have a secure university education for his
lovely daughter Daisy. His daughter is now 13 years old. She plans
to enroll at the University of Professional Studies, Accra in 5
years, and it should take her 4 years to complete her education.
Currently, the cost per year (for everything – her food, clothing,
tuition, books, transportation, and so forth) is GH¢ 12,000 per
year. This cost is expected to remain constant throughout the
four-year university education. The daughter recently received GH¢
7,500 from her grandfather’s (King David’s) estate; this money will
be invested at a rate of 8% to help meet the costs of Daisy’s
education. The rest of the costs will be met by money King Solomon
will deposit in a savings account which also earns 8 percent
compound interest per year. He will make 5 equal deposits into the
account, one deposit per annum starting one year from now until his
daughter starts university. These deposits will begin one year from
now. (Assume that school fees are paid at the beginning of the
year).
Again, King Solomon is interested in buying a bond issued by Zenzo
Pharma Ltd. Zenzo Pharma intends to use the proceeds of the bonds
to finance the production of its new vaccine for COVID 19. The bond
has a face value of GH¢10,000 at a coupon rate of 12% and a term to
maturity of 10 years. The bond expects to pay coupons annually.
Included in the bond indenture are call and sinking fund
provisions. The required rate of return on the market for bonds
with similar features is 18% per annum. Your boss had asked you to
advice King Solomon based on the information he provided
Required
a. Explain to King Solomon what financial markets mean and which
three (3) financial instruments he can invest
in.
b. To the nearest cedi, how much must he save during each of the
next 10 years (with equal deposits being made at the end of each
year, beginning a year from today) to meet his retirement goal?
(Note: Neither the amount he saves nor the amount he withdraws
upon
retirement is a growing
annuity.)
c. What will be the present value of the cost of 4 years of
education at the time the daughter
Daisy turns
18?
d. What will be the value of the GH¢ 7,500 that Daisy received from
her grandfather’s estate
when she starts college at
18?
e. If King Solomon is planning to make the first of 5 deposits one
year from now, how large must each deposit be for him to able to
put his daughter through
college?
f. Explain to King Solomon what call provisions and sinking fund
provisions are and how these provisions are expected to affect the
risk of the
bond
g. Which value will you place on a bond of Zenzo Pharma
Ltd?
In: Finance
Consider a small town with two coffee shops, Star and Buck. If
Star’s price is ?? per cup of coffee and Buck’s price is ?? per cup
of coffee, then their respective monthly sales, ?? hundred cups of
coffee and ?? hundred cups of coffee, are given by the following
equations:
?? = 5 − ?? + ??
?? = 15 − ?? + ??
It costs $8 for both Star and Buck to produce a cup of coffee and
it costs $10 for Buck to produce a cup of coffee.
a. Are these two coffee shops producing substitute or
complementary products? How can you verify that based on the demand
equations?
b. For each of the coffee shop, write the profit as a function of
?? and ??.
c. Find each coffee shop’s best-response function.
d. Find the Nash Equilibrium price in this game.
e. Consider a twisted version of the above game: suppose that Star
has an option to advertise its coffee. This advertisement will cost
Star $5,000 if Star decides to use it, and it will change the
demand equations as:
?? = 12 − 0.5?? + 0.5??
?? = 10 − ?? + 0.5??
The marginal cost of each cup of coffee remains the same. Star has
to determine whether to use the advertisement and the price of its
coffee simultaneously. Find the Nash Equilibrium price in this
game. (Hint: this is still a simultaneous game. Star can choose to
advertise or not and its price, Buck can only choose its
price.)
In: Economics
There are 4 big houses in my home town. They are made from these materials: red marbles, green marbles, white marbles and blue marbles. We know the following facts:
Who lives where, and what is their house made from?
In: Statistics and Probability
a) What is the probability of winning the grand prize?
b) What is the probability of winning the lesser prize?
c) If a lottery ticket costs $1, what is the expected value of playing this lottery?
In: Advanced Math