Homework 2

1. Problem 4.6 The monthly sales for Telco Batteries, Inc., were as follows:
Month Sales
January 20
February 21
March 15
April 14
May 13
June 16
July 17
August 18
September 20
October 20
November 21
December 23
a) Plot the monthly sales data
b) Forecast January sales using each of the following:
Naive method
A 3-month moving average
A 6-month weighted average using 1,1,1,2,2, and 3, with the heaviest weights applied to the most recent months
Exponential smoothing equal to 3 and a September forecast of 18
A trend projection
c) With the data given, which method would allow you to forecast next March’s sales?
2. Problem 4.47 The owner of a restaurant serving Continental-style entrees was interested in studying ordering patterns of patrons for the Friday -to-Saturday weekend time period. Records were maintained that indicated the demand for dessert during the same time 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 entree was ordered. The results are as follows:
Gender
Dessert Ordered Male Female Total
Yes 96 40 136
No 224 240 464
Total 320 280 600

Beef Entree
Dessert Ordered Yes No Total
Yes 71 65 136
No 116 348 464
Total 187 413 600
A waiter approaches a table to take an order for dessert. What is the probability that the first customer to order at the table
a. orders a dessert?
b. orders a dessert or has ordered a beef entree?
c. is a female and does not order a dessert?
d. is a female or does not order a dessert?
e. Suppose the first person from whom the waiter takes the dessert order is a female. What is the probability that she does not order dessert?
f. Are gender and ordering dessert independent?
g. Is ordering a beef entree independent of whether the person orders dessert?
Problem 5.12 you are trying to develop a strategy for investing in two different stocks. The anticipated annual return for a $1,000 investment in each stock under four different economic conditions has the following probability distribution
Returns
Probability Economic Condition Stock X Stock Y
0.1 Recession -100 50
0.3 Slow growth 0 150
0.3 Moderate growth 80 -20
0.3 Fast growth 150 -100
Compute the
a. expected return for stock X and for stock Y
b. standard deviation for stock X and for stock Y
c. covariance of stock X and stock Y
d. Would you invest in stock X or stock Y? Explain
Problem 5.13 Suppose that in Problem 5.12 you wanted to create a portfolio that consists of stock X and stock Y. Compute the portfolio expected return and portfolio risk for each of the following percentages invested in stock X:
a. 30%
b. 50%
c. 70%
d. On the basis of the results of (a) through (c), which portfolio would you recommend? Explain

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