Module 6 – Probability Distributions

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ECOM1000 – Analytics for Decision Making
Module 6 – Probability Distributions
Learning Outcomes
After completing this Lab/Tutorial you should be able to:
1. Recognise and apply the properties of a probability distribution
2. Calculate the expected value and variance of a probability distribution. Apply this concept to a financial context.
3. Identify situations that can be modelled by discrete distributions (Binomial, Poisson and Hypergeometric) and
calculate probabilities associated with the Binomial and Poisson Distributions.
4. Identify situations that can be modelled by continuous distributions (Normal, Uniform and Exponential) and
calculate probabilities from the normal distribution. Determine whether a set of data is normally distributed. Be
informed of the relationship between Normal and Binomial distribution.
PART 1 – Short answer questions
Question 1
A probability distribution is an equation that
A. assigns a value to the centre of the sample space.
B. assigns a value to the variability in the sample space.
C. measures outcomes and assigns values of X to the simple events.
D. associates a particular probability of occurrence with each outcome in the sample space.
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Question 2
The following table contains the probability distribution for X = the number of traffic accidents reported in a day in Perth.

a) Referring to the above distribution, the probability of three accidents is [Blank].
b) Referring to the above distribution, the probability of at least one accident is [Blank].
c) Referring to the above distribution, the mean or expected value of the number of accidents is [Blank].
d) Referring to the above distribution, the variance of the number of accidents is [Blank].
Question 3
A campus program evenly enrols undergraduate and graduate students. If a random sample of four students is selected
from the program to be interviewed about the introduction of a new fast-food outlet on the ground floor of the campus
building, what is the probability that all four students selected are undergraduate students?
A. 0.0256
B. 1.00
C. 0.0625
D. 0.16
Question 4
The Department of Commerce in a particular state has determined that the number of small businesses that declare
bankruptcy per month is approximately a Poisson distribution with a mean of 6.4. Find the probability that exactly five
bankruptcies occur next month.
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Question 5
True or False: The probability that a standard normal random variable, Z, falls between -1.50 and 0.81 is 0.7242.
A. True
B. False
Question 6
The value of the cumulative standardised normal distribution at Z is 0.6255. The value of Z is
A. 0.40.
B. 0.16.
C. 0.32.
D. 0.99.
Question 7
If we know that the length of time it takes a university student to find a parking space in the university car park follows a
Normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, find the probability that a
randomly selected university student will find a parking space in the car park in less than 3 minutes.
A. 0.3085
B. 0.3551
C. 0.2674
D. 0.1915
Question 8
In the game Wheel of Fortune, which of the following distributions can best be used to compute the probability of winning
the special vacation package in a single spin?
A. Uniform distribution.
B. Binomial distribution.
C. Exponential distribution.
D. Normal distribution.
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PART 2 – Data Exercise
Download the file titled “stock_price_2017.xlsx” from the data section in module 6. Open the file in Excel and complete the
following questions:
a) Describe the contents in this file.
b) Replicate columns D and E (financial returns)
c) Construct a time series plot of the stock prices for each stock and comment on the resulting plot
d) Construct a scatter plot of both the stock prices and comment on the resulting plot
e) Construct a time series plot of the returns for each stock and comment on the resulting plot
f) Construct a scatter plot of both the stock returns and comment on the resulting plot
g) Compute the descriptive statistics for each return.
h) Compute the covariance of the returns.
i) Construct a frequency polygon of returns? Are the returns normally distributed? Provide reasons.
j) What is expected value (mean) of the portfolio which contains equal weighting (w = 0.5) for each return?
k) What is risk (standard dev) of the portfolio which contains equal weighting (w = 0.5) for each return?
l) Briefly describe how the expected value and risk of portfolio changes as the weighting (w) changes?
PART 3 – Pearson MyLab
Please logon to MyLab and complete the following tasks.
1. Complete the homework questions based on module 6 topics.
2. Please ensure that you have finished the Mylab activities from module 1, 2, 3 and 5. These included the Candidate
agreement, Orientation questions and Homework questions (Module 1,2,3 and 5). The recorded tutorials/labs from
modules 1, 2, 3 and 5 provide a brief overview of the homework questions in Mylab.
Note: If you are having issues with obtaining access to Mylab, please re-read the instructions (available in the welcome
module). If you are still unsuccessful, please send an email to ecom1000@curtin.edu.au explaining the issue. The quiz (week
8) will be done using MyLab and will contain content from module 1 through to module 5 (inclusive). More details on this
assessment will be released in week 7 (after the submission of part 1 of the project).