STAT 344Homework 5
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Instructions:
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Deadline: November 04, 2022, at 11.59PM through Blackboard as a single PDF.
Handwritten solutions must be scanned and submitted as a PDF file.
Typed solutions are acceptable and must be submitted as a PDF file.
Do not submit hard copies in Class.
Do not submit pictures/Photos as multiple files.
Submissions that do not meet all the following criteria will not be graded:
Your solutions will grade for accuracy; all steps must be shown. The solutions are expected to be
of collegiate quality.
Each solution should be:
• Written one question per page
• written darkly.
• Should be easy to follow.
• Must show your work
Be sure that your name in the upper right-hand corner of each page.
See below options for generating a PDF for this exam, Name the file
STAT344HW5_Lastname_Firstname.
Once the PDF has been generated, please view the file to assure its legibility prior to uploading.
You will only be able to upload the file once.
Generating a PDF: Here are some options for generating a PDF:
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CamScanner – PDF Scanner App; free on Android and iOS. You can upload to Google
Drive and Dropbox directly.
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Using “Notes” app on iOS/Apple Devices:
You should practice generating a PDF at least three times prior to the submitting one. Be sure that
the file can be easily viewed on a tablet, iPad, and computer.
I strongly suggest that you create a folder on the device that you will use to store the PDFs for this
course.
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Answer all questions.
1. Consider the following continuous Joint PDF.
𝑓(𝑥, 𝑦) = 𝐾.
𝑥
𝑦!
”
In # < 𝑥 < 𝑦 𝑎𝑛𝑑 1 < 𝑦 < 2
a. Sketch the region where the PDF lies.
b. Find the value of the constant K that makes this a valid joint probability density
function
c. Find the marginal density function of Y.
d. Find the Expectation of Y.
2. Consider the following dataset.
130
55
58
97
54
96
101
77
86
87
45
75
51
100
129
64
155
111
67
78
109
151
125
93
69
66
60
139
81
50
136
113
111
94
99
80
55
55
104
200
102
66
83
96
83
62
90
91
113
97
a. Describe the shape of the data set using an appropriate graphical summary.
b. Calculate the Five number summary.
c. Calculate Mean, Variance, Range, and Interquartile range.
d. Calculate the Lower Fence and Upper Fence for Outliers.
e. Are there any outliers? If any exists, remove the outliers, re-calculate Five number
summary, Mean, Variance and Interquartile range.
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