Applied Statistics and Probability for Engineers
Applied Statistics and Probability for Engineers
6th Edition
ISBN: 9781118539712
Author: Douglas C. Montgomery
Publisher: WILEY
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Chapter 3.7, Problem 133E
To determine

Show that probability mass function of negative binomial random variable equals the probability mass function of a geometric random variable when r=1.

Show that mean and variance of negative binomial random variable equals corresponding results for a geometric random variable when r=1.

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Chapter 3 Solutions

Applied Statistics and Probability for Engineers

Ch. 3.1 - Prob. 1ECh. 3.1 - For each of the following exercises, determine the...Ch. 3.1 - For each of the following exercises, determine the...Ch. 3.1 - For each of the following exercises, determine the...Ch. 3.1 - For each of the following exercises, determine the...Ch. 3.1 - For each of the following exercises, determine the...Ch. 3.1 - Prob. 7ECh. 3.1 - For each of the following exercises, determine the...Ch. 3.1 - For each of the following exercises, determine the...Ch. 3.1 - For each of the following exercises, determine the...
Ch. 3.1 - For each of the following exercises, determine the...Ch. 3.1 - For each of the following exercises, determine the...Ch. 3.1 - For each of the following exercises, determine the...Ch. 3.1 - For each of the following exercises, determine the...Ch. 3.1 - For each of the following exercises, determine the...Ch. 3.2 - 3-16. The sample space of a random experiment is...Ch. 3.2 - For Exercises 3-17 to 3-21, verify that the...Ch. 3.2 - For Exercises 3-17 to 3-21, verify that the...Ch. 3.2 - For Exercises 3-17 to 3-21, verify that the...Ch. 3.2 - For Exercises 3-17 to 3-21, verify that the...Ch. 3.2 - For Exercises 3-17 to 3-21, verify that the...Ch. 3.2 - 3-22. Consider the hospital patients in Example...Ch. 3.2 - 3-23. An article in Knee Surgery, Sports...Ch. 3.2 - Prob. 24ECh. 3.2 - Prob. 25ECh. 3.2 - 3-26. The space shuttle flight control system...Ch. 3.2 - 3-27. A disk drive manufacturer sells storage...Ch. 3.2 - 3-28. Marketing estimates that a new instrument...Ch. 3.2 - 3-29. The distributor of a machine for cytogenics...Ch. 3.2 - 3-30. An assembly consists of two mechanical...Ch. 3.2 - 3-31. An assembly consists of three mechanical...Ch. 3.2 - 3-32. The data from 200 endothermic reactions...Ch. 3.2 - 3-33. Actual lengths of stay at a hospital’s...Ch. 3.2 - 3-34. The distribution of the time until a Web...Ch. 3.2 - 3-35 The following table shows the typical depth...Ch. 3.2 - 3-36. Consider the wafers with contamination...Ch. 3.2 - 3-37. Consider the circuit in Example 2-32. Assume...Ch. 3.3 - 3-38. Determine the cumulative distribution...Ch. 3.3 - 3-39. Determine the cumulative distribution...Ch. 3.3 - 3-40. Determine the cumulative distribution...Ch. 3.3 - 3-41. Determine the cumulative distribution...Ch. 3.3 - 3-42. Determine the cumulative distribution...Ch. 3.3 - Prob. 43ECh. 3.3 - Prob. 44ECh. 3.3 - 3-45. Determine the cumulative distribution...Ch. 3.3 - Prob. 46ECh. 3.3 - 3-47. Determine the cumulative distribution...Ch. 3.3 - 3-48. Determine the cumulative distribution...Ch. 3.3 - Verify that the following functions are cumulative...Ch. 3.3 - Verify that the following functions are cumulative...Ch. 3.3 - Verify that the following functions are cumulative...Ch. 3.3 - Verify that the following functions are cumulative...Ch. 3.3 - 3-53. Determine the cumulative distribution...Ch. 3.3 - 3-54. Determine the cumulative distribution...Ch. 3.3 - 3-55. Determine the cumulative distribution...Ch. 3.3 - 3-56. Determine the cumulative distribution...Ch. 3.4 - 3-57. If the range of X is the set {0,1,2,3,4} and...Ch. 3.4 - 3-58. Determine the mean and variance of the...Ch. 3.4 - 3-59. Determine the mean and variance of the...Ch. 3.4 - 3-60. Determine the mean and variance of the...Ch. 3.4 - 3-61. Determine the mean and variance of the...Ch. 3.4 - Prob. 62ECh. 3.4 - 3-63. Determine the mean and variance of the...Ch. 3.4 - Prob. 64ECh. 3.4 - 3-65. The range of the random variable X is [0, 1,...Ch. 3.4 - 3-66. In a NiCd battery, a fully charged cell is...Ch. 3.4 - 3-67. The space shuttle flight control system...Ch. 3.4 - 3-68. Trees are subjected to different levels of...Ch. 3.4 - 3-69. An article in the Journal of Database...Ch. 3.4 - 3-70. Calculate the mean and variance for the...Ch. 3.4 - 3-71. Calculate the mean and variance for the...Ch. 3.4 - 3-72. Calculate the mean and variance for the...Ch. 3.4 - 3-73. Calculate the mean and variance for the...Ch. 3.4 - 3-74. Calculate the mean and variance for the...Ch. 3.4 - 3-75. Calculate the mean for the random variable...Ch. 3.5 - 3-76. Let the random variable X have a discrete...Ch. 3.5 - 3-77. Let the random variable X have a discrete...Ch. 3.5 - 3-78. Thickness measurements of a coating process...Ch. 3.5 - Prob. 79ECh. 3.5 - 3-80. The lengths of plate glass parts are...Ch. 3.5 - 3-81. Assume that the wavelengths of...Ch. 3.5 - 3-82. The probability of an operator entering...Ch. 3.5 - 3-83. Suppose that X has a discrete uniform...Ch. 3.5 - 3-84. Show that for a discrete uniform random...Ch. 3.5 - 3-85. The number of pages in a PDF document you...Ch. 3.5 - 3-86. Suppose that nine-digit Social Security...Ch. 3.5 - 3-87. Suppose that 1000 seven-digit telephone...Ch. 3.5 - 3-88. The probability that data are entered...Ch. 3.5 - 3-89. Each multiple-choice question on an exam has...Ch. 3.5 - 3-90. Consider the hospital data in Example 2-8....Ch. 3.6 - 3-91. For each scenario (a)–(j), state whether or...Ch. 3.6 - 3-92. Let X be a binomial random variable with p =...Ch. 3.6 - 3-93. Let X be a binomial random variable with p =...Ch. 3.6 - 3-94. The random variable X has a binomial...Ch. 3.6 - 3-95. The random variable X has a binomial...Ch. 3.6 - 3-96. The random variable X has a binomial...Ch. 3.6 - 3-97. Sketch the probability mass function of a...Ch. 3.6 - 3-98. Determine the cumulative distribution...Ch. 3.6 - Prob. 99ECh. 3.6 - Prob. 100ECh. 3.6 - 3-101. The phone lines to an airline reservation...Ch. 3.6 - 3-102. A multiple-choice test contains 25...Ch. 3.6 - 3-103. A particularly long traffic light on your...Ch. 3.6 - 3-104. Samples of rejuvenated mitochondria are...Ch. 3.6 - Prob. 105ECh. 3.6 - 3-106. Heart failure is due to either natural...Ch. 3.6 - 3-107. A computer system uses passwords that are...Ch. 3.6 - 3-108. Samples of 20 parts from a metal punching...Ch. 3.6 - 3-109. Because all airline passengers do not show...Ch. 3.6 - 3-110. This exercise illustrates that poor quality...Ch. 3.6 - 3-111. Consider the lengths of stay at a...Ch. 3.6 - 3-112. Consider the patient data in Example 2-8....Ch. 3.6 - 3-113. Assume that a Web site changes its content...Ch. 3.6 - 3-114. Consider the endothermic reactions in...Ch. 3.6 - 3-115. The probability that a visitor to a Web...Ch. 3.6 - 3-116. Consider the circuit in Example 2-34....Ch. 3.6 - 3-117. Consider the time to recharge the flash in...Ch. 3.6 - 3-118. Consider the patient data in Example 2-8....Ch. 3.7 - 3-119. Suppose that the random variable X has a...Ch. 3.7 - Prob. 120ECh. 3.7 - 3-121. Consider a sequence of independent...Ch. 3.7 - Prob. 122ECh. 3.7 - 3-123. The probability of a successful optical...Ch. 3.7 - 3-124. In a clinical study, volunteers are tested...Ch. 3.7 - 3-125. Assume that each of your calls to a popular...Ch. 3.7 - 3-126. A player of a video game is confronted with...Ch. 3.7 - 3-127. Heart failure is due to either natural...Ch. 3.7 - 3-128. A computer system uses passwords...Ch. 3.7 - 3-129. A trading company uses eight computers to...Ch. 3.7 - 3-130. Assume that 20 parts are checked each hour...Ch. 3.7 - 3-131. A fault-tolerant system that processes...Ch. 3.7 - Prob. 132ECh. 3.7 - Prob. 133ECh. 3.7 - 3-134. Consider the endothermic reactions in...Ch. 3.7 - 3-135. A Web site randomly selects among 10...Ch. 3.7 - Prob. 136ECh. 3.7 - 3-137. Consider the time to recharge the flash in...Ch. 3.7 - 3-138. An array of 30 LED bulbs is used in an...Ch. 3.7 - Prob. 139ECh. 3.7 - 3-140. Customers visit a Web site, and the...Ch. 3.8 - 3-141. Suppose that X has a hypergeometric...Ch. 3.8 - Prob. 142ECh. 3.8 - Prob. 143ECh. 3.8 - Prob. 144ECh. 3.8 - 3-145. A research study uses 800 men under the age...Ch. 3.8 - Prob. 146ECh. 3.8 - Prob. 147ECh. 3.8 - 3-148. A state runs a lottery in which six numbers...Ch. 3.8 - Prob. 149ECh. 3.8 - 3-150. Calculate the finite population...Ch. 3.8 - 3-151. Consider the visits that result in leave...Ch. 3.8 - 3-152. Consider the nonfailed wells in Exercises...Ch. 3.8 - 3-153. Consider the semiconductor wafer data in...Ch. 3.8 - 3-154. Suppose that a healthcare provider selects...Ch. 3.8 - Prob. 155ECh. 3.8 - 3-156. A utility company might offer electrical...Ch. 3.9 - 3-157. Suppose that X has a Poisson distribution...Ch. 3.9 - Prob. 158ECh. 3.9 - Prob. 159ECh. 3.9 - 3-160. The number of telephone calls that arrive...Ch. 3.9 - 3-161. Astronomers treat the number of stars in a...Ch. 3.9 - 3-162. Data from www.centralhudsonlabs.com...Ch. 3.9 - Prob. 163ECh. 3.9 - 3-164. The number of flaws in bolts of cloth in...Ch. 3.9 - Prob. 165ECh. 3.9 - 3-166. The number of cracks in a section of...Ch. 3.9 - Prob. 167ECh. 3.9 - 3-168. The number of failures of a testing...Ch. 3.9 - 3-169. The number of content changes to a Web site...Ch. 3.9 - 3-170. The number of views of a page on a Web site...Ch. 3.9 - Prob. 171ECh. 3.9 - 3-172. Orders arrive at a Web site according to a...Ch. 3.9 - 3-173. The article “An Association Between Fine...Ch. 3.9 - 3-174. Inclusions are defects in poured metal...Ch. 3 - Prob. 175SECh. 3 - 3-176. Let X denote the number of bits received in...Ch. 3 - 3-177. Batches that consist of 50 coil springs...Ch. 3 - Prob. 178SECh. 3 - 3-179. A total of 12 cells are replicated. Freshly...Ch. 3 - Prob. 180SECh. 3 - 3-181. A particularly long traffic light on your...Ch. 3 - 3-182. The probability is 0.6 that a calibration...Ch. 3 - Prob. 183SECh. 3 - 3-184. The probability that an eagle kills a...Ch. 3 - 3-185. Traffic flow is traditionally modeled as a...Ch. 3 - 3-186. A shipment of chemicals arrives in 15...Ch. 3 - Prob. 187SECh. 3 - 3-188. The probability that your call to a service...Ch. 3 - 3-189. The probability that your call to a service...Ch. 3 - 3-190. The number of messages that arrive at a Web...Ch. 3 - Prob. 191SECh. 3 - 3-192. The number of errors in a textbook follows...Ch. 3 - Prob. 193SECh. 3 - Prob. 194SECh. 3 - 3-195. In a manufacturing process that laminates...Ch. 3 - Prob. 196SECh. 3 - Prob. 197SECh. 3 - 3-198. A manufacturer of a consumer electronics...Ch. 3 - Prob. 199SECh. 3 - 3-200. The random variable X has the following...Ch. 3 - Prob. 201SECh. 3 - Prob. 202SECh. 3 - Prob. 203SECh. 3 - 3-204. An installation technician for a...Ch. 3 - Prob. 205SECh. 3 - Prob. 206SECh. 3 - 3-207. Messages arrive to a computer server...Ch. 3 - 3-208. Flaws occur in the interior of plastic used...Ch. 3 - Prob. 209SECh. 3 - Prob. 210SECh. 3 - Prob. 211SECh. 3 - Prob. 212SECh. 3 - Prob. 213SECh. 3 - Prob. 214SECh. 3 - Prob. 215SECh. 3 - Prob. 216SECh. 3 - Prob. 217SECh. 3 - Prob. 218SECh. 3 - Prob. 219SE
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