Page 42 - Applied Statistics And Probability For Engineers

c02.qxd 5/10/02 1:07 PM Page 25 RK UL 6 RK UL 6:Desktop Folder:TEMP WORK:MONTGOMERY:REVISES UPLO D CH114 FIN L:Quark Files:

2-1 SAMPLE SPACES AND EVENTS 25

DeMorgan’s laws imply that

1A ´ B2¿ A¿¨ B¿ and 1A ¨ B2¿ A¿´ B¿

Also, remember that

A ¨ B B ¨ A and A ´ B B ´ A

2-1.4 Counting Techniques (CD Only)

As sample spaces become larger, complete enumeration is difficult. Instead, counts of
the number outcomes in the sample space and in various events are often used to analyze the
random experiment. These methods are referred to as counting techniques and described on
the CD.

EXERCISES FOR SECTION 2-1

Provide a reasonable description of the sample space for each 2-11. The pH reading of a water sample to the nearest tenth
of the random experiments in Exercises 2-1 to 2-18. There can of a unit.
be more than one acceptable interpretation of each experi- 2-12. The voids in a ferrite slab are classified as small,
ment. Describe any assumptions you make. medium, or large. The number of voids in each category is
2-1. Each of three machined parts is classified as either measured by an optical inspection of a sample.
above or below the target specification for the part. 2-13. The time of a chemical reaction is recorded to the
2-2. Each of four transmitted bits is classified as either in nearest millisecond.
error or not in error. 2-14. An order for an automobile can specify either an
2-3. In the final inspection of electronic power supplies, automatic or a standard transmission, either with or without
three types of nonconformities might occur: functional, minor, air-conditioning, and any one of the four colors red, blue,
or cosmetic. Power supplies that are defective are further clas- black or white. Describe the set of possible orders for this
sified as to type of nonconformity. experiment.
2-4. In the manufacturing of digital recording tape, elec- 2-15. A sampled injection-molded part could have been
tronic testing is used to record the number of bits in error in a produced in either one of two presses and in any one of the
350-foot reel. eight cavities in each press.
2-5. In the manufacturing of digital recording tape, each of 2-16. An order for a computer system can specify memory
24 tracks is classified as containing or not containing one or of 4, 8, or 12 gigabytes, and disk storage of 200, 300, or 400
more bits in error. gigabytes. Describe the set of possible orders.
2-6. An ammeter that displays three digits is used to meas- 2-17. Calls are repeatedly placed to a busy phone line until
ure current in milliamperes. a connect is achieved.
2-7. A scale that displays two decimal places is used to 2-18. In a magnetic storage device, three attempts are made
measure material feeds in a chemical plant in tons. to read data before an error recovery procedure that reposi-
2-8. The following two questions appear on an employee tions the magnetic head is used. The error recovery procedure
survey questionnaire. Each answer is chosen from the five- attempts three repositionings before an “abort’’ message is
point scale 1 (never), 2, 3, 4, 5 (always). sent to the operator. Let
s denote the success of a read operation
Is the corporation willing to listen to and fairly evaluate
new ideas? f denote the failure of a read operation
How often are my coworkers important in my overall job F denote the failure of an error recovery procedure
performance? S denote the success of an error recovery procedure
2-9. The concentration of ozone to the nearest part per billion. A denote an abort message sent to the operator.
2-10. The time until a tranaction service is requested of a Describe the sample space of this experiment with a tree
computer to the nearest millisecond. diagram.