Page 99 - Applied statistics and probability for engineers

Section 3-4/Mean and Variance of a Discrete Random Variable 77

In Example 3-11, suppose that each e-mail message header reserves 15 kilobytes of memory
space for storage. Let the random variable Y denote the memory space reserved for all message
(
)
headers per hour (in kilobytes). Then Y = h X = 15 . Also, because h X ( ) is a linear function,
X
E Y) = 15 E X) = 15 ( . ) = 187 .5 kilobytes
12
5
(
(
and
1
85
(
(
V Y) = 15 2 V X) = 15 2 ( . ) = 416 .25 square kilobytes
Exercises FOR SECTION 3-4
Problem available in WileyPLUS at instructor’s discretion.
Tutoring problem available in WileyPLUS at instructor’s discretion
3-57. If the range of X is the set {0,1,2,3,4} and P X( = x) the number of computers that vote for a left roll when a right
= 0 2, determine the mean and variance of the random variable. roll is appropriate. What are the mean and variance of X ?
.
3-58. Determine the mean and variance of the random vari- 3-68. Trees are subjected to different levels of carbon diox-
able in Exercise 3-16. ide atmosphere with 6% of them in a minimal growth condition
3-59. Determine the mean and variance of the random vari- at 350 parts per million (ppm), 10% at 450 ppm (slow growth),
able in Exercise 3-17. 47% at 550 ppm (moderate growth), and 37% at 650 ppm (rapid
3-60. Determine the mean and variance of the random vari- growth). What are the mean and standard deviation of the carbon
able in Exercise 3-18. dioxide atmosphere (in ppm) for these trees in ppm?
3-61. Determine the mean and variance of the random vari- 3-69. An article in the Journal of Database Management
able in Exercise 3-19. [“Experimental Study of a Self-Tuning Algorithm for DBMS
3-62. Determine the mean and variance of the random vari- Buffer Pools” (2005, Vol. 16, pp. 1–20)] provided the workload
able in Exercise 3-20. used in the Transaction Processing Performance Council’s Ver-
3-63. Determine the mean and variance of the random vari- sion C On-Line Transaction Processing (TPC-C OLTP) bench-
able in Exercise 3-23. mark, which simulates a typical order entry application.
3-64. Determine the mean and variance of the random vari- The frequency of each type of transaction (in the second
able in Exercise 3-24. column) can be used as the percentage of each type of transac-
⎡
,
,
,
⎣
3-65. The range of the random variable X is 0 1 2 3, x⎤ tion. The average number of selects operations required for
⎦
where x is unknown. If each value is equally likely and the each type of transaction is shown.
mean of X is 6, determine x. (a) Determine the mean and standard deviation of the number
3-66. In a NiCd battery, a fully charged cell is composed of of selects operations for a transaction from the distribution
nickelic hydroxide. Nickel is an element that has multiple oxi- of types shown in the table.
dation states. Assume the following proportions of the states: (b) Determine the mean and standard deviation of the total
Nickel Charge Proportions Found number of operations (selects, updates,…, and joins) for a
0 0.17 transaction from the distribution of types shown in the table.
+2 0.35 3-70. Calculate the mean and variance for the random variable
+3 0.33 in Exercise 3-32.
+4 0.15 3-71. Calculate the mean and variance for the random
(a) Determine the cumulative distribution function of nickel charge. variable in Exercise 3-33.
(b) Determine the mean and variance of the nickel charge. 3-72. Calculate the mean and variance for the random variable
3-67. The space shuttle light control system called in Exercise 3-34.
Primary Avionics Software Set (PASS) uses four independ- 3-73. Calculate the mean and variance for the random variable
ent computers working in parallel. At each critical step, the in Exercise 3-35.
computers “vote” to determine the appropriate step. The 3-74. Calculate the mean and variance for the random variable
probability that a computer will ask for a roll to the left in Exercise 3-36.
when a roll to the right is appropriate is 0.0001. Let X denote 3-75. Calculate the mean for the random variable in Exercise 3-37.
Average Frequencies and Operations in TPC-C
Transaction Frequency Selects Updates Inserts Deletes Nonunique Selects Joins
New order 43 23 11 12 0 0 0
Payment 44 4.2 3 1 0 0.6 0
Order status 4 11.4 0 0 0 0.6 0
Delivery 5 130 120 0 10 0 0
Stock level 4 0 0 0 0 0 1