STAY-HOME FINAL EXAM
PSTAT 160B – Winter 2021
Jean-Pierre Fouque
Instructions:
Please submit your work as a pdf-file via Gradescope. Don’t forget to match your pages
with the problems.
Submission deadline: March 19, 2021, at noon (12 p.m. (PST)).
Academic Integrity at UCSB: “Papers, examinations, laboratory reports, and homework
must always be your own work. Cheating, plagiarism, and collusion are all forms of academic
dishonesty and are violations of the Student Conduct Code. Students found responsible for
these violations face possible suspension or dismissal from the University.”
Academic Conduct at UCSB: “It is expected that students attending the University of
California understand and subscribe to the ideal of academic integrity, and are willing to bear
individual responsibility for their work. Any work (written or otherwise) submitted to fulfill
an academic requirement must represent a students original work. Any act of academic
dishonesty, such as cheating or plagiarism, will subject a person to University disciplinary
action. Cheating includes, but is not limited to, looking at another students examination,
referring to unauthorized
notes during an exam, providing answers, having another person
take an exam for you, etc.”
This is an open notes exam in the sense that you are welcome to refer to our lecture videos,
lecture notes (Dobrow’s book), and assignment sheets, but nothing else!
This is not a collaborative exam. You are expected to take this exam in isolation with
no communication with other people. Communicating with others about the exam
problems is considered cheating.
You must show all of your work and carefully justify your answers, otherwise points
will be deducted. You may justify your answers by either writing brief sentences explaining
your reasoning or annotating your math work with brief explanations. Explicitly cite re-
sults from class when you use them and briefly explain why they are applicable.
Introduce all processes, random variables etc. you use.
Use a calculator to compute numerical values as final answers (if applicable).
Good Luck!
PSTAT 160B STAY-HOME FINAL EXAM
1. (10 points) Let pNtqtě0 be a Poisson process with parameter λ 0 and denote by S1, S2, . . .
the corresponding arrival times. Moreover, let f : R R be a bounded function.
Show that
E