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Homework #1
STAT351.001
Winter 2024
Due: Monday January 22, 2024
Include all work in a neat and well organized presentation. Grading is based on the quality,
thoroughness, and correctness of the work provided.
You do not need to print out this assignment; you may provide your work and answers on your own
separate paper (had written is sufficient). Your submission should be well-organized and legible.
Upload your solutions as a single PDF file to the “Homework 1” submission folder in our Canvas course.
Your submission should be titled “(your name) STAT351 Homework 1.”
set
Notes:
1. Show all work, points are awarded based on the quality, thoroughness, and correctness of
the work provided.
2. When referring to sets, please use proper set notation.
3. When providing probabilities provide them as numbers between 0 and 1 (not as percentages),
and keep at least 3 decimal places.
____________________________________________________________________________________
1.
You roll a fair (balanced) 6-sided dice two times, record what lands face-up.
(6pt)
Let A be the event: the sum of the face-up values is greater than or equal to 9.
Let B be the event: the difference between face-up values is less than or equal to 2.
Let C be the event: neither dice lands on the value “1”.
Compute the following probabilities.
a.
( )
b.
( ∪ )
c.
( ∩ )
d.
∩ ( ∪ )
e.
( ∩ ∩ )
____________________________________________________________________________
2.
In a particular city, A recent analysis concluded that
(6pt)
12% of all residences have detectable levels of lead in their tap water and
8% of all residences have detectable levels of radon in their basement or sub-foundation.
Additionally, the analysis noted that 5% of all residences have both, detectable levels of
radon, and detectable levels of lead.
One residence is randomly selected. Determine each of the following.
a.
Hat is the probability that the randomly selected residence has neither detectable
levels of lead nor detectable levels of radon.
b.
What is the probability that the randomly selected residence has either detectable
levels of lead or detectable levels of radon (or has detectible levels of both).
c.
What is the probability that the randomly selected residence has exactly one of
these concerns (either detectable levels of lead or detectable levels of radon but
not both).
__________________________________________________________________________
3.
For a particular probability experiment, the sample space is:
(4pt)
Ω = {1,2,3,4,5,6,7,8,9}
Additional information:
– The even number outcomes are equally likely:
({2}) = ({4}) = ({6}) = ({8})
a.
x
p(x)
–
The odd number outcomes are equally likely:
({1}) = ({3}) = ({5}) = ({7}) = ({9})
–
It is twice as likely that the experiment results in an even number as an odd
number.
({2,4,6,8}) = 2 ({1,3,5,7,9})
For each possible value (1 through 9) calculate its probability. Fill out the
following table where x = the result of the experiment. Round each to 3 decimal
places.
1
b.
2
3
4
5
6
7
8
9
Find the probability that this experiment results in a number greater than 4.
_________________________________________________________________________
4.
Refresher on Summation Notation. Evaluate each of the following:
(4pt)
a.
b.
When k is a constant:
c.
When k is a constant:
( + 2)
d.
Let ( ) =
Compute:
( )
for = 0,1,2,3
0
otherwise
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