MATH 118: Statistics and Probability Homework #4 solved

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Problem 1: (10+10+10+10+10+10+40 = 100 points)
WARNING: Please show your OWN work. Any cheating can be easily detected and will not be graded.
For the question, please follow the file called airplane crashes.txt while reading the text below.
In each year from 1993 to 2012, the number of airplane crashes in airline companies were counted. The data was
collected from 14 different airline companies. The numbers of crashes for the airline companies are indicated
in 14 columns following the year column. Assume that the number of crashes per airline company per year is a
random variable having a Poisson(λ) and that the number of crashes in different airline company or in different
years are independent.
(Note: You should implement a code for your calculations for each following subproblem. You are free to use
any programming languages (Python, R, C, C++, Java) and their related library.)
(a) Give a table how many cases occur for all companies between 1993 and 2012 for each number of crashes (#
of Crashes).
Hint: When you check the file you will see: # of Crashes = {0, 1, 2, 3, 4}.
(b) Estimate λ from the given data.
(c) Update Table 1 in Table 2 with Poisson predicted cases with the estimated λ.
(d) Draw a barplot for the actual cases (Table 2 in column 2) and the predicted cases (Table 2 column 3) with
respect to # of crashes. You should put the figure.
1
– Homework #4 2
\# of
Crashes
\# of cases
in all company
between the years
0
1
2
3
4
Table 1: Actual cases
\# of
Crashes
\# of cases
in all companies
between the years
Predicted \# of cases
in all companies
between the years
0
1
2
3
4
Table 2: Actual vs. Predicted Cases
(e) According to the barplot in (c), does the poisson distribution fit the data well? Compare the values of the
actual cases and the values of the poisson predicted cases, and write your opinions about performance of the
distribution.
(f) According to your estimations above, write your opinions considering your barplot and Table 2. Do you
think that airplane transportation is dangerous for us? Whether yes or no, explain your reason.
(g) Paste your code that you implemented for the subproblems above. Do not forget to write comments on
your code.
Example:
• The common code block for all subproblems
Paste here. Your code should read the file and compute other things which the following subproblems
need.
• The code block for (a)
Paste here. Your code should compute the values in Table 1 column 2.
• The code block for (b)
Paste here. Your code should compute λ.
• The code block for (c)
Paste here. Your code should compute the values in Table 2 column 3.
• The code block for (d)
Paste here. Your code should draw the barplot.