Let X1,X2,...,Xn be a random sample from a uniform distribution on the interval (0,a). Recall that the maximum likelihood estimator (MLE) of a is ˆ a = max(Xi).
a) Let Y = max(Xi). Use the fact that Y ≤ y if and only if each Xi ≤ y to derive the cumulative distribution function of Y.
b) Find the probability density function of Y from cdf.
c) Use the obtained pdf to show that MLE for a (ˆ a = max(Xi)) is biased.
d) Say I would like to consider another estimator for a, I will call it ˆ b = 2 ¯ X. Is it unbiased estimator of a (show)? How you can explain someone without calculations why ˆ b = 2 ¯ X is a reasonable estimator of a?
e) Based on the result in (c), I will propose to use unbiased estimator for a instead of ˆ a = max(Xi), say ˆ c = n+1 n max(Xi). Given that the relative efficiency of any two unbiased estimators ˆ b,ˆ c is the ratio of their variances
V ar(ˆ b) V ar(ˆ c)
,
explain which of these two unbiased estimators is more efficient. You can obtain the V ar(ˆ c) = V ar(n+1 n max(Xi)) from V ar(ˆ a) = Var(Y ). The variance of the Y = max(Xi) is
Var(Y ) =
n/( (n + 1)^2(n + 2))*a^2

Consider the utility functions of three individuals: u(x) = x^1/2, v(x) = ln x, and h(x) = x – 0.01 x², where x represents wealth.

Consider also the following lotteries: X = (w₀ + x₁, w₀ + x_2, w₀ + x_{3; ¼, ½, ¼ )} = (4, 16, 25; ¼, ½, ¼), where w₀ = $2, and lottery Y in which w₁ = $10, so that Y = (12, 24, 33; ¼, ½, ¼). Note that Y = X + (10; 1)

1. Tell whether u(x), v(x) and h(x) are risk averse, risk neutral or risk lovers individuals.

2. Compare individuals u(x) and v(x) with respect to their degree of risk aversion. Tell who is more risk averse.

3. Calculate the risk premium of individuals u(x) and v(x) with respect to lottery X. Did you obtain that the risk premium of v((x) is larger than that of u(x)? Is that result expected? Why?

4. Compare the risk premium of individual u(x) with respect to lotteries X and Y. Did you obtain that the risk premium with respect to lottery X is larger than that with respect to Y? Is that result expected? Why?

5. Compare the risk premium of individual h(x) with respect to lotteries X and Y. Did you obtain that the risk premium with respect to lottery X is larger than that with respect to Y? Is that result expected? Why?

1. Determine the current in the circuit by calculating the current in the resistor. Note: We will use I (and V_R since it has the same phase) for reference throughout our analysis (V_R/R = I).

2. Determine the capacitance of the circuit from its reactance, the current calculated above, and the frequency of the source (V_C/I = X_C).

3. Determine the inductance of the circuit from three different voltage measurements, the current calculated in step 1, and the frequency of the source, following the instructions below carefully (this can be complicated).

1. Determine the phase of V_LR with respect to V_R using the law of cosines (V_Lr²= V_LR² + V_R² – 2V_LRV_R cos(α)).

2. Determine the fraction of V_LR due to V_L alone (V_L = V_LRsin(α)).

3. Determine the inductance of the circuit from its reactance using the current determined in step 1 and the V_L determined above (V_L/I =X_L).

4. Determine the loss in the inductor and write it as a resistance using the current found in step 1

            (V_r = V_LRcos(α) – V_R and r = V_r/I).

4. Determine the phase between the source voltage and the current (φ = tan^-1 [(V_L – V_C)/(V_R+V_r)]).

5. Calculate the resonant frequency of the circuit from the values you determined for L and C

Assume you wish to evaluate the risk and return behaviors associated with various combinations of assets V and W under three assumed degrees of​ correlation: perfect​ positive, uncorrelated, and perfect negative. The following average return and risk values were calculated for these​ assets:
Asset   Average Return, {r}}   Risk (Standard Deviation), s
V   7.6%   4.7%
W   13.2%   9.4%


a. If the returns of assets V and W are perfectly positively correlated​ (correlation coefficient equals plus 1 ​), describe the range of​ (1) return and​ (2) risk associated with all possible portfolio combinations.
​(1) Range of expected​ return: between % and % ​(Round to one decimal​ place.)

​(2) Range of the​ risk: between % and % ​(Round to one decimal​ place.)

b. If the returns of assets V and W are uncorrelated​ (correlation coefficient equals 0 ​), describe the approximate range of ​(1​) return and​ (2) risk associated with all possible portfolio combinations.

​(1) Range of expected​ return: between % and % ​(Round to one decimal​ place.)

​(2) Range of the​ risk: between % and % ​(Round to one decimal​ place.)

c. If the returns of assets V and W are perfectly negatively correlated​ (correlation coefficient equals negative 1 ​), describe the range of​ (1) return and​ (2) risk associated with all possible portfolio combinations.

​(1) Range of expected​ return: between % and % ​(Round to one decimal​ place.)

​(2) Range of the​ risk: between % and % ​(Round to one decimal​ place.)

Swift code

import Foundation

protocol TaksPerformer {

func doAThing()

}

class Employee: TaksPerformer {

let name: String

var boss: Boss?

init(name: String) {

self.name = name

}

func doAThing() {

print("\(name) is doing a thing")

}

}

class Boss {

var employee: Employee

let name: String

init(name: String, employee: Employee) {

self.name = name

self.employee = employee

employee.boss = self

}

func actLikeABoss() {

employee.doAThing()

}

}

// 1)

// A) What is wrong with the current implementation of Boss and Employee, why is it wrong, and how can we demonstrate that there is an issue?

//

// B) What pattern discussed in class does the Boss - Employee relationship remind you of? Give an example of the discussed pattern.

//

// C) Create a Person class that has the following property:

// let name: String

// Now have Employee and Boss inherit from Person

//

// D) You realize that there are speciffic tasks you would like an employee to perform. All tasks look like this:

// func makeCoffe(_ name: String) {

// print("\(name) made coffe")

// }

//

// func writeReport(_ name: String) {

// print("\(name) wrote a report")

// }

// Modify Boss, Employee and TaskPerformer in a way that a Boss can be instantiated with the following constructor:

// Boss(name: "Bossman", employee: anEmployee, tasks: [makeCoffe, writeReport])

// The employee instance should perform the tasks.

Write a Java program to do the following with your name. This can all be done in the main() method.

1. Create a String variable called myName and assign your personal name to it. Use proper capitalization for a legal name. I.e. String myName = "Billy Bob";

2. Load myName with the upper case version of itself and display the result.

3. Load myName with the lower case version of itself and display the result.

4. Capitalize the first letter of each given name in the lowercased name and display the result. Load the result into myName. Hint: This is not a single method call. You will need a loop to perform this. Hint: The substring method will be very helpful as you should likely build a new string result. Avoid magic number references. This solution should work with any proper name.

5. Using the value of the variable myName from step 4:

a.Display the Initials of the name. ( This may require a Loop)
b.Use the trim methd on myName and store the results into myName.
c.Display the size of the name
// Using Billy Bob as the name - here are the expected results:

My name in upper case is BILLY BOB.

My name in lower case is billy bob.

My name capitalized is Billy Bob.

My initials are BB.

The length of my name is 9.

Accounting Errors

Shannon Corporation began operations on January 1, 2016. Financial statements for the years ended December 31, 2016 and 2017, contained the following errors:

In addition, on December 31, 2017, fully depreciated machinery was sold for $10,800 cash, but the sale was not recorded until 2018. There were no other errors during 2016 or 2017, and no corrections have been made for any of the errors.

Ignoring income taxes, what is the total effect of the errors on 2017 net income?

a.Net income overstated by $5,800

b.Net income overstated by $11,000

c.Net income overstated by $14,200

d.Net income understated by $1,800

• Assume you are working on budgeting for the room department of your hotel.
• Assume the hotel’s ‘Room Revenue (Sales)’ was $1,640,000 during 2016. Based on the lodging forecast report, you expect the ‘Room Revenue (Sales)’ to increase by 3.7% next year.
• Assume the ‘Guest Supplies’ expenses (variable costs) from the room department was $250,000 during 2016. For 2017, this variable cost will remain at the same percentage of the Room Revenue (Sales) as experienced in 2016.
• Assume the ‘Salaries’ expenses (fixed costs) from the room department was $280,000 during 2016. For 2017, this fixed cost will increase by 2% due to the expected increase in living expenses in this area.

1. What will be the budgeted ‘Room Revenue (Sales)’ for 2017?

2. What will be the budgeted ‘Guest Supplies’ expenses for 2017?

3. What will be the budgeted ‘Salaries’ expenses for 2017?

On October 1, 2016, Indigo Corp. issued $960,000, 5%, 10-year bonds at face value. The bonds were dated October 1, 2016, and pay interest annually on October 1. Financial statements are prepared annually on December 31.

Prepare the journal entry to record the issuance of the bonds.

Prepare the adjusting entry to record the accrual of interest on December 31, 2016.

Show the balance sheet presentation of bonds payable and bond interest payable on December 31, 2016.

Prepare the journal entry to record the payment of interest on October 1, 2017.

Prepare the adjusting entry to record the accrual of interest on December 31, 2017.

Assume that on January 1, 2018, Indigo pays the accrued bond interest and calls the bonds. The call price is 104. Record the payment of interest and redemption of the bonds.

On January 1, 2016, Flash and Dash Company adopted a healthcare plan for its retired employees. To determine eligibility for benefits, the company retroactively gives credit to the date of hire for each employee. The following information is available about the plan: Service cost $30,000 Accumulated postretirement benefit obligation (1/1/16) 120,000 Expected return on plan assets 0 Amortization of Prior service cost 10,000 Payments to retired employees during 2016 5,000 Interest rate 10% Average remaining service period of active plan participants (1/1/16) 12 years Required: 1. Compute the OPRB expense for 2016 if the company uses the average remaining service life to amortize the prior service cost. 2. Prepare all the required journal entries for 2016 if the plan is not funded.