University of Texas, Dallas
STAT 3355
Final Exam
of
STAT 3355 Introduction to Data Analysis
Due: N/A
December 1, 2022
DON’T TURN THE PAGE UNTIL YOU’RE READY TO BEGIN THE EXAM.
Instructions:
1. You will have THREE hours to complete this exam.
2. You must take this exam DURING ONE SITTING, although a break is permitted.
3. There are THREE problems
...[Show More]
Final Exam
of
STAT 3355 Introduction to Data Analysis
Due: N/A
December 1, 2022
DON’T TURN THE PAGE UNTIL YOU’RE READY TO BEGIN THE EXAM.
Instructions:
1. You will have THREE hours to complete this exam.
2. You must take this exam DURING ONE SITTING, although a break is permitted.
3. There are THREE problems on the test, totaling 30 points.
4. Open text and open notes. NO INTERNET. Make you you download any attached
datasets on eLearning before starting the exam.
5. You may hand write parts that do not require R. Combine multiple pdf’s into ONE file
and then submit to eLearning (only ONE attempt).
6. Calculators/statistical software packages are permitted for calculation purposes.
7. You must NOT DISCUSS this exam with anyone except the instructor and TA.
8. You must state and sign the UTD Honor Code on next page.
1
The Pledge: As a Comet, I pledge honesty, integrity, and service in all
that I do.
Signature:
Printed Name:
Date Exam Taken:
Start and End Time Exam Taken:
2
Problem 1
Poisson distribution is a discrete probability distribution that expresses the probability of
a given number of events occurring in a fixed interval of time if these events occur with
a known constant rate and independently of the time since the last event. For instance, a
local government keeping track of the amount of COVID-19 confirmed cases reported each
day may notice that an average number of new daily cases is 10. Without loss of generality,
we may assume that the number of new daily cases obeys a Poisson distribution with p.m.f.
pX(x) = e-λλx
x! .
Question 1.1 (5 points)
If X ∼ Poi(λ), then E[X] = Var(X) = λ (NO NEED TO DERIVE THESE). Suppose
X1; X2; : : : ; Xn is a sample from a Poisson distribution with parameter λ. Write down the
Central Limit Theorem and show the derivation of 95% confidence interval of λ in terms
of n and X¯. Hint: if a continuous r.v. X ∼ N(0; 1), then P (-1:96 ≤ X ≤ 1:96) = 0:95.
Question 1.2 (5 points)
Suppose we recorded the number of new daily cases in the past seven days, and obtained
the numbers: 9, 9, 12, 8, 11, 15, and 10. If we assume this sample is i.i.d. from a Poisson
distribution, then what is the 95% confidence interval of λ? How do you interpret this
result
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