BUEC 232-08-1
Homework Assignment 4.
DUE DATE: March 7 (Friday) 5:00 pm
Please submit your assignment to the Drop-box.
(Using Excel is optional)
1. The owner of a restaurant serving Continental-style entrées was interested in studying
ordering patterns of patrons for the weekend period. Records were maintained that
indicated the demand for dessert during the same period. The owner decided to study two
other variables, along with whether a dessert was ordered: the gender of the individual
and whether a beef entrée was ordered. The results for 600 customers are as follows:
Gender
Dessert Ordered
Male
Female
YES
96
40
NO
224
240
Beef Entrée
Dessert Ordered
YES
NO
YES
71
65
NO
116
348
(Note: these two tables are for the same 600 customers).
(i) For a randomly select customer, what is the probability that this customer
(a) Orders a dessert?
(b) Orders a dessert or a beef entrée?
(c) Is a female and does not order a dessert?
(d) Does not order dessert given that this person is a lady?
(ii)
(a) Are gender and ordering dessert independent? Why or Why not?
(b) Is ordering a beef entrée independent of whether the person orders
dessert? Why or Why not?
2. The editor of a publishing company is trying to decide whether to publish a
proposed business statistics textbook. Information on previous textbooks published
indicates that 10% are huge successes, 20% are modest successes, 40% break-even,
and 30% are losers. However, before publishing decision is made, the book will be
reviewed. In the past, 99% of huge successes, 70% of moderate successes, 40% of
the break-even, and 20% of losers received favorable reviews. Note that the
information implies that a published book may have received either the favorable
review or unfavorable review. Based on these data, graph a probability tree and
compute the following probabilities:
(a) What is the probability that a randomly selected published textbook receive
favorable review?
(b) Given that the book is a modest success, what is the probability that this
book received unfavorable review?
3. You are trying to develop a strategy for investing in two different stocks. The
anticipated annual return for $1000 investment in each stock under four different
economic conditions has the following probability distribution:
Returns
Probability
Economic Condition
Stock X (in $’s)
Stock Y (in $’s)
0.1
Recession
- 50
- 100
0.3
Slow growth
20
50
0.4
Moderate growth
100
130
0.2
Fast growth
150
200
Note: Return means the net change in your initial investment ($1000) after a year, for
example, Return=-100 (negative return), it means that after one year, your wealth become
$900.
(a) Compute the expected return for stock X and for stock Y.
(b) Compute the standard deviation for stock X and for stock Y.
(c) If the correlation between X and Y is 0.98, compute the mean and the standard
deviation of a simple portfolio with 50% of the initial investment in Stock X and
50% of the initial investment in Stock Y.