Assignment2_Winter2024 V3

.docx

School

Carleton University *

*We aren’t endorsed by this school

Course

151

Subject

Statistics

Date

Feb 20, 2024

Type

docx

Pages

Uploaded by MegaRiver12287 on coursehero.com

STAT 151 STAT 151 Assignment 2 Due date : refer to the Course Outline Purposes This assignment has two parts. The following questions assess your ability to identify the sample space of a chance experiment, calculate probabilities using the equally likely outcome model, and the addition, complementation, conditional probability, and multiplication rules, determine if two events are independent by calculation, and apply counting rules. This assignment also assesses your understanding of discrete probability distributions, your ability to find the mean (expected value) and the standard deviation of a discrete random variable and your ability to identify and work with binomial random variables. The second part assesses your ability to use R commander to compute the probabilities listed above. Instructions For every assignment in this course, you are required to complete the questions or tasks in Part A by hand. This means that to do any calculation or drawing, you will NOT use R commander or any computer application. That is, you are meant to do the calculations manually with a non- programmable scientific calculator and use a pen or pencil to draw figures or build a distribution table on paper (or on an iPad/tablet). Then you will submit a photo of your written solution using the appropriate submission box on the corresponding Crowdmark submission page. Before you complete Part B using R commander, you should read and practice the R commander steps by following the related examples in the Lab Manual and the Demos, which you can download via a link in the Course Content folder on mêskanâs. Where appropriate, units should be included in your answer. Show your calculations fully and provide a concluding sentence to your problems. Part A 1. The handedness of a group of 3 people are Ambidextrous (A), Lefthanded (L), or Righthanded (R). Suppose two people are randomly selected with replacement (that is, a person is selected, their handedness is observed and they are returned to the group of three people). Let A be the event of selecting an ambidextrous person, L be the event of selecting a lefthanded person, and R be the event of selecting a righthanded person. (a) List all possible outcomes. (2 marks) (b) List all possible outcomes for each of the following events and find the corresponding probabilities. (8 marks) 1

STAT 151 i. E1 = {Exactly 1 person of type L is drawn} ii. E2 = {The second person is right handed} iii. E3 = {At MOST one person is ambidextrous} iv. E4 = {Both people have the same handedness} (c) List all possible outcomes and find the probabilities of the following events. (12 marks: 2 for each) i. Not E3 ii. E1 & E3 iii. E1 & E4 iv. E2 & E3 v. E2 & E4 vi. E3 or E4 (d) Identify all possible pairs of events defined in part (b) that are mutually exclusive. (3 marks) (e) Verify mathematically that E2 and E4 are independent events, while E3 and E4 are not. (3 marks) 2. Suppose we select a random sample of 4 numbers between 1 and 30, sampling without replacement. (a) How many unordered samples of size 4 are possible? (2 marks) (b) What is the probability that the sum of the values in our sample is less than 14? (3 marks) 3. People can be right handed, mixed handed, or left handed: RH, MH, LH. People can also be right footed, mixed footed or left footed: RF, MF, LH. So a person can be one of 9 handedfooted possibilities: RHRF, RHMF, RHLF, MHRF, MHMF, MHLF, LHRF, LHMF, LHRF. Among a group of 1000 students you find that 600 are RHRF, 265 are RHMF, 31 are RHLF, 3 are MHRF, 17 are MHMF, 4 of them are MHLF, 14 of them are LHRF , 19 of them are LHMF, and 47 of them are LHLF. A random sample of 9 students will be selected from this group of 1000 students. Later in the course we will see how these figures compare to the figures found in Table 3 in the 2016 research paper “Footedness Is Associated with Self-reported Sporting Performance and Motor Abilities in the General Population”, by Ulrich S. Tran and Martin Voracek https://www.frontiersin.org/articles/10.3389/fpsyg.2016.01199/full , but for now we will limit ourselves to questions regarding sampling choices. 2

STAT 151 (a) How many different samples are possible? (2 marks) (b) How many different samples of size 9 are possible subject to the constraint that no 2 students may have the same handedfooted result? (2 marks) (c) What is the probability that a random sample of 9 students from this group has no two students with the same handedfooted result? (2 marks) 4. A certain lottery sells 10 million tickets for $2 each. Let X denote your winnings upon purchasing 1 ticket, and suppose X has the following probability distribution x P ( X = x ) $ 2,000,000 1 10,000,000 $ 100,000 10 10,000,000 $ 1,000 20 10,000,000 $ 0 9,999,969 10,000,000 (a) What is the expected value of X. (2 marks) (b) Since each ticket costs $2, define Y=X-2 to be your profit from purchasing 1 ticket. Compute and interpret the expected value of Y. (2 marks) (c) What is the probability that you have no winnings if you purchase a ticket? (So you win $0 on your ticket) (1 mark) (d) Suppose you purchase 30 tickets. Let T be the total winnings among all 30 tickets. What is the probability that you have 30 losses? (So no ticket wins any money). For simplicity, assume independence. (2 marks) (e) What is the probability you win any money among all the 30 tickets (so at least one ticket wins an amount). (3 marks) 5. At 11 pm one evening, the Queen discovers that her carrying case of bespoke gloves has gone missing after her recent return from a trip overseas. She is due to leave on a 30-day trip to Korea at 5 pm the next night. Her dresser Angela contacts her glove maker 3

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

Recommended textbooks for you

Calculus For The Life Sciences

Calculus

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:Pearson Addison Wesley,

College Algebra

Algebra

ISBN:9781938168383

Author:Jay Abramson

Publisher:OpenStax

SEE MORE TEXTBOOKS