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Chapter 7: Problem 6

List the simple events associated with each experiment. Data concerning durable goods orders are obtained each month by an economist. A record is kept for a 1 -yr period of any increase \((i)\), decrease \((d)\), or unchanged movement \((u)\) in the number of durable goods orders for each month as compared with the number of such orders in the same month of the previous year.

Short Answer

Expert verified
The simple events for this experiment are all possible combinations of increases (i), decreases (d), and unchanged movements (u) in the monthly durable goods orders over a one-year period (12 months). There are 3 possible outcomes for each month, resulting in a total of \( 3^{12} \) simple events for this experiment.

Step by step solution

01

Understanding the experiment

In this problem, we have an experiment where monthly durable goods orders are observed for a one-year period. For each month, there are three possible outcomes: the number of orders increases (i), decreases (d), or remains the same (u) compared to the same month's orders the previous year.
02

Identifying total months

In a year, there are 12 months. We need to find the possible simple events for each month, considering the three possible outcomes for each month's record.
03

Listing simple events for each month

As we have 3 outcomes (i, d, and u) for each month and 12 months in a year, we can consider every combination of these outcomes for each month. We can list all the simple events for a one-year period as a sequence \( (E_1, E_2, E_3, ..., E_{12}) \), where each \( E_i \) can take one of the possible outcomes, i.e., i, d, or u. Based on this idea, there are \( 3^{12} \) possible combinations of outcomes for the 12 months.
04

Summary of the results

In conclusion, we have identified that there are 3 possible outcomes (i, d, and u) for each of the 12 months in a year, which gives a total of \( 3^{12} \) simple events for this experiment with durable goods orders.

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