What is the relevant outcome space of the random variable Y ?

Econ 41 Review

  1. Discrete Random Variables. Suppose that we are interested in the number of cups of coffee drank by a
    (randomly selected) student at UCLA. This quantity can be represented as a random variable Y with
    probability mass function:
    pY (a) =

    
    
    1
    4
    if a ∈ {0, 1, 2}
    1
    8
    if a = 3
    3
    32 if a = 4
    c if a = 5
    0 otherwise
    ,
    where c is an unknown constant.
    (a) Explain why the number of cups of coffee drank in a day by a randomly selected student at UCLA
    is a random variable.
    (b) What is the relevant outcome space of the random variable Y ?
    (c) Explain what the distribution of this random variable represents. In other words distribution of
    Y assigns a probability to any subset of the outcome space. How do we interpret this probability?
    (d) Solve for c. (Hint: Recall that PY (OY ) = 1 so that P
    a∈OY
    pY (a) must equal one).
    (e) What is the probability that a randomly selected student at UCLA drinks at least 3 cups of coffee
    a day, PY (Y ≥ 3)?
    (f) What is the expected number of cups of coffee drank per day for a randomly selected student at
    UCLA?
  2. Continuous Random Variables. Suppose that we are interested in the income of a randomly selected
    Angeleno. The distribution of incomes (in tens of thousands of dollars) for residents of Los Angeles
    can be described as a random variable, X, with the following pdf.
    fX(a) =



    0.11 − ca if 0 ≤ a ≤ 10
    0 otherwise
    ,
    where c is an unkown constant.
    1
    Page 2
    (a) What is the outcome space of X, OX?
    (b) Using the relationship
    PX(l ≤ X ≤ m) = Z m
    l
    fX(a) da,
    explain why the pdf must always be weakly positive, fX(a) ≥ 0, for any a ∈ R.
    (c) Because PX(OX) = 1 we must have that R 10
    0
    fX(a) da = 1. Using this fact, solve for c.
    (d) What is the expected value of X, E[X]?
    (e) What is the variance of X, Var(X)?
  3. Variance and Covariance. Let Y be a random variable representing income (in tens of thousands of
    dollars) and X be a random variable representing years of education. Suppose that the marginal
    distribution of X is described by its probability mass function
    pX(x) =

    
    
    0.05 if x ∈ {1, 2, . . . , 12}
    0.09 if x ∈ {13, 14, 15, 16}
    0.04 if x ∈ {17}
    0 otherwise
    .
    The marginal distribution of Y is described by its probability density function
    fY (y) =



    0.1 if 0 ≤ y ≤ 10
    0 otherwise
    .
    (a) What is the expectation of Y , E[Y ]? What is its variance, Var(Y )?
    (b) What is the expectation of X, E[X]? What is its variance, Var(X)?
    (c) Using E[Y X] = 60 compute the covariance between Y and X, Cov(X, Y ).
    (d) Calculate the correlation coefficient between X and Y .
    ρY X =
    Cov(X, Y )
    σXσY
    .
    (e) What does this covariance tell us about the relationship between education levels and income? Is
    there a positive or negative association?
    (f) Should we interpret this result as a causal relationship between education and income? What are
    some reasons we may want to refrain from this interpretation?
    (g) (Challenge) A common inequality used in econometrics is the Cauchy-Schwarz inequality. It
    states that, for any random variables X and Y , and any functions g(·) and h(·),

    E[g(X)h(Y )]

    ≤
    p
    E[g
    2(X)]p
    E[h
    2(Y )].
    Use this inequality to show why the correlation coefficient is bounded between negative one and
    Page 3
    one, −1 ≤ ρXY ≤ 1. (Hint: Try g(x) = x − µX and h(y) = y − µY ).
    Introduction to Single Linear Regression
  4. Useful Equalities. Recall that in deriving the form of βˆ
    1 we used the following equalities
    1
    n
    Xn
    i=1
    (Yi − Y¯ )(Xi − X¯) = 1
    n
    Xn
    i=1
    YiXi − Y¯ X¯ and 1
    n
    Xn
    i=1
    (Xi − X¯)
    2 =
    1
    n
    Xn
    i=1
    X2
    i − (X¯)
    2
    .
    Show either one of these equalities (only have to show one or the other).
  5. Assumptions for Inference. Suppose we are interested in the relationship between the size of the average
    American’s social circle, X, and whether or not they are unemployed, Y . To investigate this relationship
    we want to estimate the following regression equation1
    Y = β0 + β1X + , E[] = E[X] = 0.
    To estimate the regression coefficient parameters we collect a sample of size n, {Yi
    , Xi}
    n
    i=1. Recall
    that for valid asymptotic inference on our estimates βˆ
    0 and βˆ
    1 we require the following assumptions:
    Random Sampling, Homoskedasticity, and Rank condition.
    • Random Sampling: Assume that {Y,Xi} are independently and identically distributed from the
    population of interest, (Yi
    , Xi)
    i.i.d ∼ (Y, X).
    • Homoskedasticity: Assume that Var(|X = x) = σ
    2
    
    for all possible values of x.
    • Rank Condition: There must be at least two distinct values of X that appear in the population.
    (a) Suppose we collect our sample by only randomly surveying people on UCLA campus. Which
    assumption would be violated?
    (b) Suppose we collect our sample and find that everyone appears to have exactly one friend. Which
    assumption would be violated? Why is this a problem when computing the line of best fit through
    our sample?
    (c) Suppose random sampling, homoskedasticity, and the rank condition are all satisfied, but n = 10.
    Why might inferences based on the approximation
    βˆ
    1 − β1
    σˆβ1
    /
    √
    n
    ∼ N(0, 1)
    not be valid?
  6. Hypothesis Testing. Suppose now that we are interested in investigating the relationship between the
    size of someone’s social circle, X, and their income (in tens of thousands of dollars), Y . We want to
    estimate the following linear regression model
    Y = β0 + β1X + , E[] = E[X] = 0.
    1Recall that this regression specification corresponds to finding the line of best fit parameters β0, β1 = arg minb0,b1 E[(Y −
    b0 − b1X)
    2
    ] and defining  = Y − β0 − β1X
    Page 4
    To do so we collect a random sample of size n = 64, {Yi
    , Xi}
    64
    i=1 and find that 1
    n
    Pn
    i=1(Xi −X¯)
    2 = 100,
    1
    n
    Pn
    i=1(Yi − Y¯ )(Xi − X¯) = 225, Y¯ = 5.5, and X¯ = 1.5.
    (a) Using this information find and interpret βˆ
    1 and βˆ
    0.
    (b) After finding βˆ
    1 and βˆ
    1 describe how you would construct the estimated residuals ˆi
    .
    (c) We find that 1
    n
    Pn
    i=1 ˆ
    2
    i = 36. Use this and the result that, for n large,
    βˆ
    1 − β1
    σˆβ1
    /
    √
    n
    ∼ N(0, 1),
    to compute the (approximate) probability that, if the true value was given β1 = 0, we would see
    a value of |βˆ
    1| equal to or larger than the one that we observed.
    (d) Use this result to test, at level α = 0.1, the hypotheses
    H0 : β1 = 0 vs. H1 : β1 6= 0
    (e) Conduct this test in another fashion by constructing the test statistic t
    ∗ and comparing to either
    z0.95 = 1.64 or z0.9 = 1.24 (indicate which value you are comparing the test statistic to).
    (f) Construct a 90% confidence interval for β1. How could we use this to conduct the hypothesis test
    in part (d)?
    (g) Suppose that we find we made an error in our calculation and actually 1
    n
    Pn
    i=1(Xi − X¯)
    2 = 1. If
    all other values stayed the same, how would this change the result of the hypothesis test in part
    (d)?
Test the hypothesis that the slope is positive against the alternative that it is negative at the 5% level of significance. What is the p-value?

Single Linear Regression Theory Review

  1. Recall that we define our parameters of interest β0 and β1 as the parameters governing the “line of
    best fit” between Y and X:
    β0, β1 = arg min
    b0,b1
    E[(Y − b0 − b1X)
    2
    ]. (1)
    Once we define these parameters we define the regression error term  = Y − β0 − β1X which then
    generates the linear model
    Y = β0 + β1X + .
    (a) Using the first order conditions for β0 and β1 (set the derivatives of the right hand side of (1)
    with respect to b0 and b1 equal to zero at) show why E[] = E[X] = 0.
    (b) Using the definition of β0 and β1 as line of best fit parameters, give an intuitive explanation for
    why E[] = 0.
    Hypothesis Testing and Confidence Intervals
    In the following questions, whenver running a hypothesis test, please state the null and alternative hypotheses,
    show some work, and state the conclusion of the test.
  2. In an estimated simple regression model based on n = 64, the estimated slope parameter, βˆ
    1, is 0.310
    and the standard error of βˆ
    1 is 0.082.
    (a) What is ˆσ
    2
    β1
    ? Recall σβ1
    is the terms such that, approximately for large n,
    √
    n(βˆ
    1 − β1) ∼ N(0, σβ1
    ).
    (b) Test the hypothesis that the slope is zero against the alternative that it is not at the 1% level of
    significance (α = 0.01).
    (c) Test the hypothesis that the slope is negative against the alternative that it is positive at the 1%
    level of significance (α = 0.01).
    (d) Test the hypothesis that the slope is positive against the alternative that it is negative at the 5%
    level of significance. What is the p-value?
    1
Create a matrix detailing a variety of multimedia, technology, games, apps, and other technological tools for teaching reading and writing to struggling readers and writers.

Staying current on technology is an essential aspect of being an educator. Today’s students are digital natives, and they often respond better to media than to traditional methods of teaching. Having a strong technology repertoire is important.

Create a matrix detailing a variety of multimedia, technology, games, apps, and other technological tools for teaching reading and writing to struggling readers and writers. Include five tools/media/apps and address the following, in 100-200 words per tool:

App/technology tool description, app/technology location (online, offline through software, through a game console, etc.), and the cost.
Age level or academic level for which the technology is appropriate.
Advantages of using the technology.
Drawbacks to using the technology.
Rationalize why struggling students may benefit from the app/technology tool.
Additionally, write a 250-500 word overview of the contents of the matrix, describing how you will implement technology in your ELA classroom. Justify which of these technologies you think will be most beneficial and describe how you might convince an administrator to help you acquire the technology.

Support the matrix and summary with 3-5 resources.

While APA format is not required for the body of this assignment, solid academic writing is expected, and in-text citations and references should be presented using APA documentation guidelines, which can be found in the APA Style Guide, located in the Student Success Center

Identify one example of an organization that created value for itself through outsourcing part of its supply chain.

Discussion: Benefits and Risks of Outsourcing the Global
Supply Chain
Globalization has created many opportunities for organizations. There are
many advantages and ways to create value through outsourcing portions of
one’s global supply chain. For each opportunity, there are also many ways for
the project to run into problems.
In your initial post, address the following:
• Identify one example of an organization that created value for itself
through outsourcing part of its supply chain. Provide a link to one
resource.
o Identify the benefit that occurred.
o How did this benefit help the organization create value? Who was
the value created for—the organization, or the customer?

Choose three cases you believe have been most important in the development/evolution of juvenile justice and why.

Table 10.2 outlines important juvenile cases throughout history. Choose three cases you believe have been most important in the development/evolution of juvenile justice and why.

Requirements:

·  2-3 pages double spaced

·  Use at least two reliable sources other than the text (not Wikipedia)

Create your own top five essentials of leadership communication. Share why you feel these are important and how as a leader you can help others succeed through these five essentials.

Prior to beginning work on this discussion, read the Five Essentials of Leadership Communication (Links to an external site.).

Create your own top five essentials of leadership communication. Share why you feel these are important and how as a leader you can help others succeed through these five essentials. Your discussion post should be 250 words.

How has the advent of digital communication including direct-to-customer and social media, impacted traditional agency revenue models

Do online research related to broad trends in Advertising / PR / Strategic Communications Industry trends and changes in business, specifically the impact of digital on traditional agency models. 

Discuss the following: 

  • How has the advent of digital communication including direct-to-customer and social media, impacted traditional agency revenue models
  • What new kinds of agencies and marketing partners have emerged as a result of these changes
  • What has been the roles and behaviors of the big holding companies (Omnicom, Interpublic, etc.) in the last 20 years to cope with these changes
  • How has advertising talent (creative, media, strategy, etc) responded to the evolving agency marketplace    

You are expected to post a blog giving your thoughts on the blog topic but do not use “I” in your writing.  

500 words minimum

What did you learn in terms of leadership communication from this speech?

Prior to beginning work on this discussion, read the article Leadership Communication: Reflecting, Engaging, and Innovating (Links to an external site.) and choose one of the following speeches found on YouTube or listed on the Top 100 Speeches (Links to an external site.) of the 20th century by rank:

Listen to the audio or read the transcript and share the key points illustrated in the speech. What made the speech so memorable? What were the main takeaways? What did you learn in terms of leadership communication from this speech? Share attributes that you could incorporate into your own leadership communication. Your discussion post should be 250 words.

Analyze the background of the federal income tax system.

Introduction

Tax credits work to lower taxpayer liability rather than provide refund incentives. A tax credit is subtracted directly from the taxpayer’s tax obligation, providing equal relief to all taxpayers. This can make the credit more valuable than a deduction taken during the filing process.

There are credits for foreign taxes paid, child and dependent care expenses, and for the elderly or disabled; credits for education, retirement savings contributions, and residential energy; and child tax credit, adoption, retirement savings, and earned income.

Note: The assessments in this course are presented in a sequence and must be completed in order. In Assessments 2-5, you will work step-by-step toward completing a 1040 tax return and all the necessary related forms, based on a provided scenario. Do not complete Assessment 5 until you have submitted and received faculty feedback for Assessment 4.

Preparation

This assessment will require significant research and critical thinking to complete each required form successfully. An incorrect entry on one form will create incorrect entries in other forms.

There are two parts to this assessment. Be sure to complete both parts and submit the necessary materials.

  • Part 1: Determine eligible tax credits by completing official worksheets.
  • Part 2: Complete Schedule A and the 1040.

Scenario

Jacob and Taylor Weaver, ages 45 and 42 respectively, are married and are filing jointly in 2021.

  • They have three children, Ashley, age 9; Patrick, age 6; and John, age 17.
    • Social Security numbers are: Jacob, 222-33-4444; Taylor, 555-66-7777; Ashley, 888-99-1234; Patrick, 789-56-4321; John, 123-45-6789.
  • Taylor works part-time as a paralegal.
    • She earned $31,000 in 2021.
  • Income Taxes: $4,200 withheld.
  • Interest received from Local Bank: $6,575.
  • Estimated tax payments: $25,000.
    • $350 paid with their 2020 state tax return.
  • Jacob and Taylor bought their first house in 2021.
    • Home mortgage interest: $12,246.
    • Property tax: $12,230.
  • Federal income withholding: $2,350.
  • Charities: $4,500.
  • $435 to rent a moving truck.
  • $8,000 to put new siding on the house.
  • $11,600 for child care expenses ($5,800 for each child).
    • It was paid to Lil Tigers Daycare, 1115 S. Garrison St., Muncie, IN 47305 (EIN 98-7654321).
  • Taylor is a part-time student at Ball State University in Muncie.
    • She received a 1098-T indicating tuition and fees for 2021 in the amount of $6,011.
  • Health insurance for the family, through Taylor’s job, cost $7,500 for all 12 months of 2021.
    • They paid deductibles and co-payments of $2,550.

Instructions

  • Read the information provided in the scenario above.
  • Download the following tax forms and instructions from IRS.gov:
    • 1040.
    • Schedule A.
    • Schedule 1.
    • Schedule 3.
    • 2441.
    • 8863.
Part 1

Use the information in the scenario, on IRS.gov, and in the interactive IRS tools to interpret official rules and instructions to determine available tax credits.

  • Complete an official worksheet for each tax credit to demonstrate eligibility.
  • Submit each tax credit worksheet.
Part 2

Use the information in the scenario, on IRS.gov, and in the interactive IRS tools to Interpret official rules and instructions to complete the following:

  • Complete Schedule A.
  • Enter data from Schedule A into the 1040.
  • Apply the rules and tax tables to calculate the tax owed and the amount of any refund.
  • Submit Schedule A and the completed 1040.

Competencies Measured

By successfully completing this assessment, you will demonstrate your proficiency in the following course competencies and assessment criteria:

  • Competency 1: Analyze the background of the federal income tax system.
    • Interpret official rules and instructions to record correct entries on tax forms.
  • Competency 2: Analyze the basics of individual income tax return preparation.
    • Analyze tax rules to complete tax credit worksheets to prove eligibility.
    • Apply laws and rules to correctly enter data on Schedule A.
    • Apply rules and tax tables to record the correct tax owed on the 1040.
    • Calculate the amount of a refund on the 1040.
Calculate what can be deducted on a final income tax return.

Preparation

Tax regulations are in a state of constant change. Being able to locate, correctly interpret, and apply the information to a problem is a highly valued skill. Consider each problem and research the applicable tax regulations to answer the questions.

Instructions

For this assessment, complete the following:

  • Download Assessment 6 Problems [DOCX].
  • Using the primary source of IRS.gov and the IRS Interactive Tax Assistant and Tax Trails, locate and interpret regulations and publications that relate to each problem.
  • Record your answers to the problems in a Word document.
  • Provide an explanation for each answer, including any related calculations and evidence.
  • Include the following criteria from the scoring guide in your responses.
    • Calculate the initial basis, allowed losses, and ending at-risk amounts.
    • Explain how to treat a loss on a federal income tax return.
    • Calculate what can be deducted on a final income tax return.
    • Calculate the loss disallowed by at-risk rules and how much of the loss is disallowed by passive loss rules.
    • Explain the tax effect in a specified scenario for the last year and the current year.
    • Calculate itemized deductions for AMT purposes and identify the amount of the AMT adjustment.
  • Submit the Word document containing your answers to the problems and the explanations for your answers.

Competencies Measured

By successfully completing this assessment, you will demonstrate your proficiency in the following course competencies and assessment criteria:

  • Competency 1: Analyze the background of the federal income tax system.
    • Explain the tax effect in a specified scenario for the last year and the current year.
  • Competency 2: Analyze the basics of individual income tax return preparation.
    • Calculate the initial basis, allowed losses, and ending at-risk amounts.
    • Explain how to treat a loss on a federal income tax return.
    • Calculate what can be deducted on a final income tax return.
    • Calculate the loss disallowed by at-risk rules and how much of the loss is disallowed by the passive loss rules.
    • Calculate itemized deductions for AMT purposes and identify the amount of the AMT adjustment.
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