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(ISOM111)[2008](sum)midterm~2546^_10370.pdf
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ISMT111 Business Statistics
Midterm Examination
For L5 only
17 October 2008

Directions
1) Answer ALL FIVE questions. Marks are shown in square brackets.
2) There are 4 pages in this examination paper, which includes a normal table. Check to make sure you have a complete set and notify the invigilator immediately if part of it is missing.
3) Key formulas are provided separately.
4) Calculator may be used in this examination.
5) You are given TWO HOURS to complete this examination. Do not begin until you are told to do so.
Question 1: [16 Marks]
The relative change of a stock market index is defined to be
Index today -Index yesterday
Relative Change = .
Index yesterday
The histogram of relative changes for Heng Seng Index in 2006 is given below. .

(a)
Please find the class width used in this histogram

(b)
Please describe the important features of the histogram.

(c)
If someone invested in Hong Kong stock market in 2006, do you think he would have a profit or a loss? Please explain briefly.

(d)
What can you say about large daily gains or losses in Hong Kong stock market in 2006? (relative changes > 2% or < -2% are considered to be large)



Question 2: [20 Marks]
In the past, a company spent 90% of its advertising budget on TV commercials and only 10% on other alternatives such as event marketing, word-of-mouth campaign, and internet-based marketing. Recognizing a new trend, the marketing manager put forward a proposal to change the allocation to 60% for TV advertising and 40% for other alternatives. In a separate proposal, the manager proposed three levels (high, median, low) of total advertising budget. He estimates the probabilities for different outcomes of the budget proposals as follows.
Allocation of advertising budget
Budget level Old (90% TV, 10% others) New (60% TV, 40% others)
High 0.3 0.2
Median 0.2 0.1
Low 0.1 0.1

(a)
What is the probability that the new budget allocation proposal for spending more on non-TV alternatives will be rejected?

(b)
Given that the new allocation is approved, what is the conditional probability that high budget level will be adopted?

(c)
Assume that an either high or median level of budget is approved, what is the conditional probability of approving the new allocation?

(d)
What is the expected percentage of budget spending on TV commercial?



Question 3: (continue from Question 2) [20 Marks]
Suppose the high, median, and low budget levels correspond to 3, 2.5 and 2 million dollars, respectively.
(a)
Let the random variable X denote the proportion of budget on TV advertising. Please find the variance of X.

(b)
Let the random variable Y denote the budget amount approved. What is the expected value of Y?

(c)
Let the random variable Z be the budget amount available for TV advertising. How do you express Z in terms of X and Y?

(d)
Please find the p