Statistical Inference I: J. Lee Assignment 1 Problem 1. An exam has 10 multiple choice questions where each question has 5 possible answers. (a) If student goes into exam completely unprepared and guesses on all 10, what is the probability of getting at least 5 answers right? (b) Suppose for each question, the student has probability .60 of knowing the answer, and the student randomly guesses on the remaining questions that he/she does not know. Assuming independence of each question, what is the probability of getting at least 5 answers right? Problem 2. Suppose that A and B are mutually exclusive events for which P (A) = 0.35 and P (B) = 0.51. What is the probability that (a) either A or B occurs; (b) A occurs but B does not; (c) both A and B occur; (d) neither A nor B occurs? Problem 3. Consider two events, A and B. You are told that P (A) = 0.75 and that P (B) = 0.81. (a) What is the maximum possible value for P (A∩B)? Justify. (b) What is the minimum possible value for P (A∩B)? Justify. (c) What is the maximum possible value for P (A∪B)? Justify. (d) What is the minimum possible value for P (A∪B)? Justify. Problem 4. A row of 15 cars is stopped at a traffic light. 6 of them are Toyotas, 7 are Hondas, and 2 are Mercedes. Assuming they are ordered randomly, we want to compute the probability that the fifth car in the row is a Mercedes. (a) Describe the sample space, S, you would use to solve this problem. Make sure to define any notation you use to describe elements of the sample space. (b) Compute the probability that the fifth car is a Mercedes. Problem 5. A bookstore receives six boxes of books per month on six random days of each month. Suppose that two of those boxes are from one publisher, two from another publisher, and the remaining two from a third publisher. Our goal is to compute the probability that the last two boxes of books received last month are from the same publisher. (a) Describe the sample space, S, you would use to solve this problem. Make sure to define any notation you use to describe elements of the sample space. (b) Compute the probability that the last two boxes of books received last month are from the same publisher. Problem 6. Consider an experiment in which two fair dice are rolled. What is the conditional probability that at least one lands on 6, given that the dice land on different numbers? Problem 7. Suppose that 5 percent of men and 0.25 percent of women are color-blind. A color-blind person is chosen at random. What is the probability of this person being male? Assume that there are an equal number of males and females. Problem 8. A woman has agreed to participate in an ESP experiment. She is asked to pick, randomly, two distinct integers between 1 and 6 (inclusive). (a) What is the probability that the first number she picks is 3 and that the second number is greater than 4? (b) What is the probability that both numbers are less than 3? (c) What is the probability that both n.

1. Statistical Inference I: J. Lee Assignment 1
Problem 1. An exam has 10 multiple choice questions where
each question has 5 possible answers.
(a) If student goes into exam completely unprepared and
guesses on all 10, what is the probability of
getting at least 5 answers right?
(b) Suppose for each question, the student has probability .60 of
knowing the answer, and the student
randomly guesses on the remaining questions that he/she does
not know. Assuming independence of
each question, what is the probability of getting at least 5
answers right?
Problem 2. Suppose that A and B are mutually exclusive events
for which P (A) = 0.35 and P (B) = 0.51.
What is the probability that
(a) either A or B occurs;
(b) A occurs but B does not;
(c) both A and B occur;
(d) neither A nor B occurs?
Problem 3. Consider two events, A and B. You are told that P
(A) = 0.75 and that P (B) = 0.81.
(a) What is the maximum possible value for P (A∩B)? Justify.

2. (b) What is the minimum possible value for P (A∩B)? Justify.
(c) What is the maximum possible value for P (A∪ B)? Justify.
(d) What is the minimum possible value for P (A∪ B)? Justify.
Problem 4. A row of 15 cars is stopped at a traffic light. 6 of
them are Toyotas, 7 are Hondas, and 2 are
Mercedes. Assuming they are ordered randomly, we want to
compute the probability that the fifth car in
the row is a Mercedes.
(a) Describe the sample space, S, you would use to solve this
problem. Make sure to define any notation
you use to describe elements of the sample space.
(b) Compute the probability that the fifth car is a Mercedes.
Problem 5. A bookstore receives six boxes of books per month
on six random days of each month. Suppose
that two of those boxes are from one publisher, two from
another publisher, and the remaining two from a
third publisher. Our goal is to compute the probability that the
last two boxes of books received last month
are from the same publisher.
(a) Describe the sample space, S, you would use to solve this
problem. Make sure to define any notation
you use to describe elements of the sample space.
(b) Compute the probability that the last two boxes of books
received last month are from the same
publisher.

3. Problem 6. Consider an experiment in which two fair dice are
rolled. What is the conditional probability
that at least one lands on 6, given that the dice land on different
numbers?
Problem 7. Suppose that 5 percent of men and 0.25 percent of
women are color-blind. A color-blind person
is chosen at random. What is the probability of this person
being male? Assume that there are an equal
number of males and females.
Problem 8. A woman has agreed to participate in an ESP
experiment. She is asked to pick, randomly, two
distinct integers between 1 and 6 (inclusive).
(a) What is the probability that the first number she picks is 3
and that the second number is greater than
4?
(b) What is the probability that both numbers are less than 3?
(c) What is the probability that both numbers are greater than 3?
Problem 9.
(a) A gambler has in his pocket two fair coins and one two-
headed coin. He selects one of the coins at
random; when he flips it, it shows heads. What is the
probability that it is a fair coin?
(b) Suppose that he flips the same coin a second time and again
it shows heads. What is now the probability
that it is a fair coin?
(c) Suppose that he flips the same coin a third time and it shows

4. tails. What is now the probability that
it is a fair coin?
Problem 10. I tell you that, for two events A and B, P (A) =
0.70, P (B|A) = 0.5, and that A and B are
independent. For each statement, say “True”, “False”, or “Can’t
Tell”, and give a reason for your answer.
(a) A and B are mutually exclusive
(b) A and A∪ B are independent
(c) P (B) = P (A|B)
(d) P (A|B) < P (B|A)
(e) P (B) ≤ P (A)
Managing Organisations (MNG10247)
Assignment 2
Title: Assignment 2 – Reflective Essay (Internal Process)
Marks: 25 (which is 25% of the unit grade)
Due: Prior to 11pm on Friday 8th April (week 6), 2016
Purpose:
This assignment aims to develop students’ understanding of the
Internal Process management model through the integration of
theory and practice. Additionally, it continues to further
develop the skill of reflective practice, which students were
introduced to in assignment 1.
Task
Students are to write a reflective essay (max 750
words[footnoteRef:1]) which details how one of the Internal
Process Management Competencies has been ‘experienced’ in

5. the workplace. [1: In the UIG it is stated that the maximum
word limit for the assignment is 500 words. The minimum word
limit is 500 and the maximum is 750.]
Note: students need not have direct involvement with the
management competency but simply observed its development,
implementation or outcome in an organisational setting.
Students with no workplace experience on which to base their
essay will need to identify and interview someone who can
provide the required first-hand insight.
Formatting
The single document submitted for this assignment is to contain
the following components and formatting features:
a) Assignment ‘Coversheet’ (document is available in the
Assignment file on Blackboard).
b) Assignment ‘Coverpage’[footnoteRef:2] identifying the unit
name & code, assignment title, student name & ID, and the
essay word count (note: Reference List content does not
contribute to the word count). [2: The assignment ‘Coversheet’
and ‘Coverpage’ contain similar information but they are
separate documents and fulfil different purposes. The coverpage
is something that each individual student develops themselves.
]
c) Content; i.e. your Reflective Essay.
i. Both in-text and reference list skills must be demonstrated
(use SCU Library’s Harvard Referencing style Guide).
ii. The essay is to include at least three distinct references from
academic journals. You may cite your textbook and sources
identified in it but they do not contribute to the reference count.
Quoting is not permitted. Paraphrase the information obtained
from the various sources.
d) Reference List
Adopt the following formatting features for the paper:
· Apply page numbers. Page 1 comes after your coverpage.
· Font style: Times New Roman, 12pt, justified, 1½ line

6. spacing.
· Margins - top and bottom to be 2.54cm. Left and right to be
2.54cm. No page boarders.
· Spelling - specify Australian English language/grammar when
running your spell-check.
· Writing and grammar should conform to the standards of a
professional report.
Structure and style of the Essay
The document ‘Reflective Writing – Quick Guide’ (available in
the Assignment 1 folder on BlackBoard) highlights two
different ways to structure the essay. Either approach is
acceptable.
Develop a catchy title which highlights (surreptitiously) the
focus of your Essay.
The aim is to write an interesting story which clearly illustrates
a good example (positive or negative) of the way in which a
particular Management Competency has been applied in an
organisational context. It is important that the key concepts are
presented in a logical manner so that the essay has good ‘flow’.
The essay should effectively blend your personal observation
with support from academic publications (i.e. ideas or research
findings). Focus on objectivity rather than subjectivity.
It is important that you use pseudonyms to protect the identity
of the organisation and the individuals concerned.
This is not a Creative Writing exercise. The objective is not to
write a dramatic script so avoid, as much as possible, using
overly emotional language and tone.
Submit Process
All assignments are to be submitted through‘Turn-it-in,’ which
can be accessed from the ‘Assignment 2’ folder on Blackboard.
The link will be activated in week 4 and you can submit the
assignment at any time leading up to the due date.
The file you submit should be labelled in the following manner:
Surname, initial, student code, MNG10247, asmt 2

7. For example – Gillett, P, 012345, MNG10247, asmt 2
Feedback
Assignments submitted by the due date will be marked and
feedback given within two weeks. Feedback will include a
marking rubric and a copy of the assignment document with
electronic comments from the marker.
Marking Criteria:
See below
Marking Criteria:
A. Quality of writing
(weight 32%)
1) Unsatisfactory. The writing is ineffective due to numerous
spelling and/or grammatical errors.
2) Pass. Proof-read the final document to identify and correct
minor errors in spelling and grammar. Plan for and undertake
additional drafts to improve the quality of your written work.
3) Credit. A good standard of writing is provided (no spelling
errors) however there is room for improvement in terms of
higher-order writing skills (e.g. vocabulary and sentence
structure).
4) Distinction. Higher-order writing skills are evident in parts.
Greater consistency will improve the overall quality of your
work.
5) HD. The quality of writing is exceptional. Well done.
B. Essay Content

8. (weight 40%)
1) Unsatisfactory. Details of the Management Competency and
your personal account of its application to an organisational
context are largely inaccurate or ambiguous.
2) Pass. The essay content demonstrates a basic understanding
of the Management Competency however it is predominantly
descriptive. Further personal insight is required to show how
the competency has been experienced in an organisational
context.
3) Credit. The essay provides a good example of how the
Management Competency is applied in an organisational
context. Expand on the analysis (depth or breadth) of your
personal experience to show a stronger level of understanding.
4) Distinction. Your personal experience of the Management
Competency is thorough and informative. Management theory is
partially integrated into the discussion.
5) HD. The essay provides a very effective and distinct example
of the Management Competency and its practical application to
an organisation context. Personal observation is substantially
and effectively integrated with Management theory. Well done.
C. Formatting & Referencing
(weight 28%.)
1) Unsatisfactory. The assignment document is
unprofessionally presented and/or the required number of
references is not provided.
2) Pass. The assignment paper is generally well presented but at
least one formatting feature has not been adopted and there is at
least one error with the referencing technique.
3) Credit. All the required formatting features are provided
however there is at least one error with the referencing
technique.

9. 4) Distinction. The correct referencing technique has been
adopted however at least one formatting feature that has not
been adopted.
5) HD. All required formatting features are provided and there
are no errors with the referencing technique.
U
P
C
D
HD
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5
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7
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B.
2
5
7
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10
C.
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10. Statistical Inference I: J. Lee Assignment 2
Problem 1. In your pocket, you have 1 dime, 2 nickels, and 2
pennies. You select 2 coins at random
(without replacement). Let X represent the amount (in cents)
that you select from your pocket.
(a) Give (explicitly) the probability mass function for X. Also
show a plot of it.
(b) Give (explicitly) the cdf, F(x), for X. Also show a plot of it.
(c) How much money do you expect to draw from your pocket?
Problem 2. Consider a random variable X whose distribution
function (cdf) is given by
FX (x) =
0 if x < −2
0.1 if − 2 ≤ x < 1.1
0.3 if 1.1 ≤ x < 2
0.6 if 2 ≤ x < 3
1 if x ≥ 3.
(a) Give the probability mass function, p(x), of X, explicitly.
(b) Compute P(2 < X < 3).
(c) Compute P(X ≥ 3).
(d) Compute P(X ≥ 3 | X ≥ 0).

11. (e) What is the cdf (distribution function) of Y = X2? (be
explicit!)
(f) Compute E(X). Also compute E(X3 − cos πX).
Problem 3. Six men and five women apply for a job at Alpha,
Inc. Three of the applicants are selected (at
random) for interviews. Let X denote the number of women in
the interview pool.
(a) Give the probability mass function, p(x), of X, explicitly.
(b) Find the probability that either one or two women are in the
interview pool.
(c) How many women do you expect to be in the interview
pool?
Problem 4. Consider a random variable X whose probability
mass function (pmf) is given by
p(x) =
p if x = −1.9
0.1 if x = −0.1
0.3 if x = 20p
p if x = 3
4p if x = 4
0 otherwise.
(a) What is p?
(b) Compute P(1.9 ≤ |X| ≤ 3).

12. 1
(c) What is F(0)? What is F(2)? What is F(F(3.1))?
(Here, F(·) denotes the distribution function (cdf) for X)
(d) Sketch a plot of the function F(x).
(Make sure to label the coordinates on the axes!)
(e) What is P(2X − 3 ≤ 4 | X ≥ 2.0)?
(f) Compute E(X).
(g) Compute E(F(X)).
2