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:
• CamScanner – PDF Scanner App; free on Android and iOS. You can upload to Google
Drive and Dropbox directly.
• 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.
course.
Answer all questions.
1. Consider the following continuous Joint PDF.
�(�, �) = �.
�
�!
In
”
#
< � < � ��� 1 < � < 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 45 109 136 102
55 75 151 113 66
58 51 125 111 83
97 100 93 94 96
54 129 69 99 83
96 64 66 80 62
101 155 60 55 90
77 111 139 55 91
86 67 81 104 113
87 78 50 200 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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