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UCLA ID: −−−−−−−−− TA Session: −−−−− LAST ..., Exams of Probability and Statistics

Stat 100A -Intro Probability. Old exam. J. Sanchez. UCLA Department of ... Cheat sheet can have only formulas and definitions, no solved problems, ...

Typology: Exams

2022/2023

Uploaded on 05/11/2023

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Stat 100A -Intro Probability
Old exam J. Sanchez
UCLA Department of Statistics
MUST DO BEFORE STARTING EXAM
UCLA ID: −−−−−−−−−TA Session: −−−−−
LAST NAME (Please, PRINT): −− (Put ID on your desk)
FIRST NAME: −−−−−−−−−
SIGNATURE (In English): −−−−−−−−−
(a) WRITE AND MARK YOUR NAME AND ID ON THE SCANTRON.
(b) WRITE THE COLOR OF THE EXAM ON THE TOP OF THE SCANTRON, IN NUMBER 2 PENCIL.
(c) WRITE YOUR NAME ON ALL SIDES OF THE CHEAT SHEET, TOP RIGHT HAND CORNER.
MAKE SURE YOUR CHEAT SHEET IS STAPLED THROUGHOUT THE WHOLE EXAM.
(d) DO NOT DETACH ANY PAGES FROM THIS EXAM. EXAM MUST STAY STAPLED DURING THE
WHOLE EXAM.
(e) PUT ALL YOUR BELONGINGS INSIDE YOUR BACKPACK UNDER THE CHAIR.
(f) ONLY ID, NUMBER 2 PENCIL AND PEN, ERASER, SCIENTIFIC CALCULATOR, SCANTRO-
NAND CHEAT SHEET ALLOWED IN THE EXAM.
(g) PUT DOWN THE TABLES ON YOUR RIGHT AND LEFT. ALL ITEMS MUST BE ON YOUR DESK.
Other important Instructions–Read. Points lost for not following directions OR 0 POINTS IN THE EXAM,
and further consequences.
Closed books, closed notes. Material covered is up to last day of lecture before the exam.
Students without a cheat sheet must let the professor know that do not have one before the exam and sit
on the front row of the exam room.
You must be silent in the exam room throughout the whole time that you are in the room, from the
moment you enter until the end.
Only scientific calculator allowed for computations. You may not use your phone or any other electronic
device as calculator. Graphics calculators are not allowed. No exceptions.
Phones and other electronic devices must be placed inside your backpack and not accessed again until
you are out of the room. While in the classroom, they must be in your backpack and your backpack
on the floor under the chair. If you do not have a backpack, you must put the items on the front desk.
Iwatches and other devices are not allowed either. Phones or devices in pockets will lead to big loss of
points in the exam. It is not worth the risk.
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Old exam J. Sanchez UCLA Department of Statistics MUST DO BEFORE STARTING EXAM

UCLA ID: − − − − − − − − − TA Session: − − − − −

LAST NAME (Please, PRINT): − − − − −− (Put ID on your desk)

FIRST NAME: − − − − − − − − −−

SIGNATURE (In English): − − − − − − − − −−

(a) WRITE AND MARK YOUR NAME AND ID ON THE SCANTRON.

(b) WRITE THE COLOR OF THE EXAM ON THE TOP OF THE SCANTRON, IN NUMBER 2 PENCIL.

(c) WRITE YOUR NAME ON ALL SIDES OF THE CHEAT SHEET, TOP RIGHT HAND CORNER. MAKE SURE YOUR CHEAT SHEET IS STAPLED THROUGHOUT THE WHOLE EXAM.

(d) DO NOT DETACH ANY PAGES FROM THIS EXAM. EXAM MUST STAY STAPLED DURING THE WHOLE EXAM.

(e) PUT ALL YOUR BELONGINGS INSIDE YOUR BACKPACK UNDER THE CHAIR.

(f) ONLY ID, NUMBER 2 PENCIL AND PEN, ERASER, SCIENTIFIC CALCULATOR, SCANTRO- NAND CHEAT SHEET ALLOWED IN THE EXAM.

(g) PUT DOWN THE TABLES ON YOUR RIGHT AND LEFT. ALL ITEMS MUST BE ON YOUR DESK.

Other important Instructions–Read. Points lost for not following directions OR 0 POINTS IN THE EXAM, and further consequences.

  • Closed books, closed notes. Material covered is up to last day of lecture before the exam.
  • Students without a cheat sheet must let the professor know that do not have one before the exam and sit on the front row of the exam room.
  • You must be silent in the exam room throughout the whole time that you are in the room, from the moment you enter until the end.
  • Only scientific calculator allowed for computations. You may not use your phone or any other electronic device as calculator. Graphics calculators are not allowed. No exceptions.
  • Phones and other electronic devices must be placed inside your backpack and not accessed again until you are out of the room. While in the classroom, they must be in your backpack and your backpack on the floor under the chair. If you do not have a backpack, you must put the items on the front desk. Iwatches and other devices are not allowed either. Phones or devices in pockets will lead to big loss of points in the exam. It is not worth the risk.

Old exam J. Sanchez UCLA Department of Statistics

  • Answer for multiple choice questions will be marked in scantron AND the exam. Work will not be read. Failure to mark your name, ID or some answers will result in point deduction from the exam grade. This is the second time you do a test. So no more grace period on this.
  • The scantron, together with the cheat sheet will be inserted inside the exam before you turn in the exam.
  • Left handed students must sit in a seat for left-handed students. The professor will tell students where to sit. Please, let the professor know that you are left handed once seated and she will indicate where to move.
  • ID must be ready to show BEFORE and at all times during the exam. NO ID, no exam.
  • This midterm must show your individual work. Talking to others during the midterm, not adhering to the above, sharing information or breaking any other aspect of the student code of conduct at UCLA will not be tolerated and will be referred to the Dean of Students office. You can not exchange papers or information. All your things must be on the floor. You may not use the empty seats next to you to put things. Put the tables down. Honor code applies.
  • Cheat sheet can have only formulas and definitions, no solved problems, no examples of any kind, no proofs, no numerical examples, no intermediate steps and no drawings or graphs of any kind.YOUR NAME MUST BE ON CHEAT SHEET AT ALL TIMES. Be ready to show your cheat sheet when the instructor requests it. The cheat sheet must be written all in English. Cheat sheets that do not comply will result in lower grade in the exam. You may have four pages, i.e., two sides of two 11 by 8 sheet, STAPLED. If you do not have a cheat sheet, you must tell the professor at the beginning of the exam and sit on the front row of the room.
  • The examples of distributions that you are allowed to have on the exam will be attached to the exam. Those are the only examples you may have.
  • You may not speak to each other in the exam room. Wait until you are out of the room.

Old exam J. Sanchez UCLA Department of Statistics

(c) 0.

(d) 0.

(e) 0.

Solution 3. X = number of defectives in a sample of 3,

P(X > 1) =

2

1

3

3

0

3

Question 4. Rebuilt ignition systems leave an aircraft rework facility at a rate of three per hour, on average. The assembly line needs four ignition systems in the next hour. What is the probability that they will be available? (Note: making an appropriate assumption about the distribution of the random variable is part of this exercise).

(a) 0.

(b) 0.

(c) 0.

(d) 1

(e) 0.

Solution 4. Let Y= number of ignition systems that leave the facility at a given hour. Then Y can be assumed to be Poisson with parameter λ = 3.

P(Y ≥ 4) = 1 − P(Y ≤ 3) = 1 − 3

(^0) e− 3 0! −^

31 e−^3 1! − 3 (^2) e− 3 2! −^

33 e−^3 3! =^0.^3527681

Question 5. ApplewithWindows provides free examination of its products for seven days. If not completely sat- isfied, a customer can return the product within that period and get a full refund. According to past records of the company, an average of 2 of every 10 products sold by this company are returned for a refund. Using the Poisson probability distribution formula, find the probability that exactly 6 of the 40 products sold by this company on a given day will be returned for a refund.

(a) 0.

(b) 0.

(c) 0.

(d) 0.