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代做统计作业 However, your write-up and code should reflflect your understanding of the material. As such,these should be written in your own words.
Instructions 代做统计作业
Please upload the following to Canvas, through GradeScope, by the due date:
(1) A document in PDF format containing the answers to all questions, including numerical answers,written explanations, and relevant graphs and fifigures. You must show your work. Follow the guidelines in the syllabus regarding how to include your code in your PDF submission.
You should name the fifile: YOURCNETID HW1.pdf.
Collaboration Policy: You are permitted to work together on this assignment in small groups of 2-4 students. However, your write-up and code should reflflect your understanding of the material. As such,these should be written in your own words. Additionally, please indicate at the top of your write-up the names of students with which you collaborated.
Distribution of COVID-19 Vaccinations
For questions (1)-(4), consider the COVID-19 vaccination distribution in Figure 1 below, which describes the composition of vaccine receipt of the population of adults (ages 18+) residing in the United States.
Figure 1: Vaccine Composition of resident adult U.S. population
Source: Data from the Centers for Disease Control and Prevention, September 2021
1.If we were to pick a resident adult at random, what would be the probability that person is vaccinated with J&J? [1pt]
2.If we were to pick a resident adult at random, among the fully vaccinated population, what would be the probability that person is vaccinated with J&J? [1pt]
3.Let X indicate the number of doses of vaccine that a person has received. Recall that Pfifizer and Moderna have a two-dose regimen and J&J has a one-dose regimen.1 代做统计作业
(a) Construct a graph of a PMF or PDF of X. Which is it a PMF or PDF? Brieflfly explain. [2pt]
(b) Construct a graph of the CDF of X. [1pt]
(c) Calculated the expected value of X. [1pt]
(d) Calculate the variance of X (note: we are observing a population distribution of X). [1pt]
(e) Based on a visual inspection of the PMF of X you plotted in part (a), is the skewness = 0,< 0, or > 0. Brieflfly explain how you know. [1pt]
1You can assume that partially vaccinated individuals have received one dose, and, for simplicity, you can assume that no one has received a third dose.
4.Challenge question: Now suppose you learn that 6% of fully vaccinated Pfifizer recipients, 4% of fully vaccinated Moderna recipients, and 8% of fully vaccinated J&J recipients have received an extra booster dose. Calculate the expected value of this new variable that we will denote X2. [+1pt]
Additional Statistical Exercises 代做统计作业
5.Is the following function a valid PDF for a random variable X? Brieflfly explain. If it is a valid PDF, calculate F(
), where F(x) is the cumulative distribution function for X. [3pt]
6.Construct the PMF for the CDF given in Figure 2: [2pt]
7.Use the PMF you constructed to calculate: [3pts]
(a) E(X)
(b) E(X2 )
(c) V ar(X)
8.You are given the following table which describes the joint probability function between X and Y .
(a) Complete the missing cells in the table. [1pt]
(b) What is the value of P r(X = 2 and Y = L) [1pt]
(c) What is the value of P r(X = 1|Y = L) [1pt]
(d) Write the marginal PMF for Y , fy(·). [1pt]
9.You are trying to learn about your expected salary after graduation, so you collect data on annual salaries (in thousands of US$) from a small random sample of recent Harris graduates:
{74, 215, 0, 86, 102, 78}
(a) Calculate the sample mean. [1pt]
(b) Calculate the sample median. [1pt]
(c) Calculate the sample variance. [1pt]
10.A friend provides you with the following R output, where months.unemp is a variable indicating the duration of unemployment in months for a sample of displaced workers:
> quantile(fx.3a, probs = seq(.1,.9,.1))
10% 20% 30% 40% 50% 60% 70% 80% 90%
1 2 2 4 6 8 9 9 11
(a) Your friend asks you for your help in calculating the 90-50 interquantile range and the 90-10 interquantile range. Calculate those two interquantile ranges. [1pt]
(b) Next your friend asks for your help in calculating the interquartile range. Are you able to calculate it from the above R output? If no, brieflfly explain why not. If yes, calculate the interquartile range for your friend. [1pt]
Data Exercise 代做统计作业
Minimum Wage & Employment
In this problem, you will use the data from Card and Krueger’s (1994) seminal study on the effffect of a minimum wage increase on employment. They leverage a minimum wage increase in New Jersey as a natural experiment. Specififically, they compare changes in fast food employment levels in New Jersey(before and after a minimum wage increase) with changes in fast food employment over the same time period just across the state border in Pennsylvania. If you’re interested in more details, the paper is posted on Canvas.
The data set cardkrueger.csv contains the following variables:
11.Load the data into R. How many unique chain restaurants are in the sample? How many total observations are in the sample? [1pt]
12.Plot a histogram of employment from the period prior to the minimum wage increase. [1pt]
(a) What is the mean employment in this period. What is the median employment in this period?[1pt]
(b) Based on these sample statistics and the histogram, is skewness = 0, > 0, or < 0? Brieflfly explain. [1pt]
13.What value would Fˆ(29) return, where Fˆ(x) is the empirical CDF for the variable emp pre? (Note:You should exclude any missing values in the emp pre variable.) [1pt]
14.Create a variable that is equal to the difffference in employment between the two periods (subtracting emp pre from emp post.
(a) What is the mean change in employment in New Jersey? [1pt]
(b) What is the mean change in employment in Pennsylvania? [1pt]
(c) What might comparing these quantities tell us? Brieflfly explain. [1pt]
