Description
Part1) Central Limit Theorem (20 points)
The input data consists of the sequence from 1 to 20 (1:20). Show the following three
plots in a single row.
a) Show the histogram of the densities of this distribution.
b) Using all samples of this data of size 2, show the histogram of the densities of the
sample means.
c) Using all samples of this data of size 5, show the histogram of the densities of the
sample means.
d) Compare of means and standard deviations of the above three distributions.
Part2) Central Limit Theorem (20 points)
The data in the file queries.csv contains the number of queries Google has had each day for a one
year period (365 days). The data file is also available at
http://kalathur.com/cs544/data/queries.csv. Use this link to read the data using read.csv function
when submitting the homework.
a) Show the histogram of the distribution of the number of queries. Compute the mean and
standard deviation of the number of queries Google has had per day.
b) Draw 1000 samples of this data of size 5, show the histogram of the densities of the sample
means. Compute the mean of the sample means and the standard deviation of the sample means.
c) Draw 1000 samples of this data of size 20, show the histogram of the densities of the sample
means. Compute the mean of the sample means and the standard deviation of the sample means.
d) Compare of means and standard deviations of the above three distributions.
Part3) Central Limit Theorem – Negative Binomial distribution (20
points)
Suppose the input data follows the negative binomial distribution with the
parameters size = 5 and prob = 0.5.
a) Generate 1000 random numbers from this distribution. Show the barplot
with the proportions of the distinct values of this distribution.
b) With samples sizes of 10, 20, 30, and 40, generate the data for 5000
samples using the same distribution. Show the histograms of the densities
of the sample means. Use a 2 x 2 layout.
c) Compare of means and standard deviations of the data from a) with the
four sequences generated in b).
Part4) Sampling (40 points)
Use the MU284 dataset from the sampling package. Use a sample size of
20 for each of the following.
a) Show the sample drawn using simple random sampling without
replacement. Show the frequencies for each region (REG). Show the
percentages of these with respect to the entire dataset.
b) Show the sample drawn using systematic sampling. Show the
frequencies for each region (REG). Show the percentages of these with
respect to the entire dataset.
c) Calculate the inclusion probabilities using the S82 variable. Using these
values, show the sample drawn using systematic sampling. Show the
frequencies for each region (REG). Show the percentages of these with
respect to the entire dataset.
d) Order the data using the REG variable. Draw a stratified sample using
proportional sizes based on the REG variable. Show the frequencies for
each region (REG). Show the percentages of these with respect to the
entire dataset.
e) Compare the means of RMT85 variable for these four samples with the
entire data.
Submission:
Create a folder, CS544_HW5_lastName and place the following file in this
folder.
Provide the R code, HW5_lastName.R, with each portion of the code
clearly identified by the corresponding question. Prepare a corresponding
word document by pasting the output for each question
(HW5_lastName.docx)
Archive the folder (CS544_HW5_lastName.zip). Upload the zip file to
the Assignments section of Blackboard.
