095_Prob and Stat for Eng Soln_Probability and Statistics for Engineering and the Sciences 6TH ED

095_Prob and Stat for Eng Soln_Probability and Statistics for Engineering and the Sciences 6TH ED

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CHAPTER 3 Section 3.1 1. S: FFF SFF FSF FFS FSS SFS SSF SSS X: 0 1 1 1 2 2 2 3 2. X = 1 if a randomly selected book is non-fiction and X = 0 otherwise X = 1 if a randomly selected executive is a female and X = 0 otherwise X = 1 if a randomly selected driver has automobile insurance and X = 0 otherwise 3. M = the difference between the large and the smaller outcome with possible values 0, 1, 2, 3, 4, or 5; W = 1 if the sum of the two resulting numbers is even and W = 0 otherwise, a Bernoulli random variable. 4. In my perusal of a zip code directory, I found no 00000, nor did I find any zip codes with four zeros, a fact which was not obvious. Thus possible X values are 2, 3, 4, 5 (and not 0 or 1). X = 5 for the outcome 15213, X = 4 for the outcome 44074, and X = 3 for 94322. 5. No. In the experiment in which a coin is tossed repeatedly until a H results, let Y = 1 if the experiment terminates with at most 5 tosses and Y = 0 otherwise. The sample space is infinite, yet Y has only two possible values. 6. Possible X values are1, 2, 3, 4, … (all positive integers) Outcome: RL AL RAARL RRRRL AARRL X: 2 2 5 5 5 95
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Chapter 3: Discrete Random Variables and Probability Distributions 7. a. Possible values are 0, 1, 2, …, 12; discrete b. With N = # on the list, values are 0, 1, 2, … , N; discrete c. Possible values are 1, 2, 3, 4, … ; discrete d. { x: 0< x < } if we assume that a rattlesnake can be arbitrarily short or long; not discrete e. With c = amount earned per book sold, possible values are 0, c, 2c, 3c, … , 10,000c; discrete f. { y: 0 < y < 14} since 0 is the smallest possible pH and 14 is the largest possible pH; not discrete g. With m and M denoting the minimum and maximum possible tension, respectively, possible values are { x: m < x < M }; not discrete h. Possible values are 3, 6, 9, 12, 15, … -- i.e. 3(1), 3(2), 3(3), 3(4), …giving a first element, etc,; discrete 8. Y = 3 : SSS; Y = 4: FSSS; Y = 5: FFSSS, SFSSS; Y = 6: SSFSSS, SFFSSS, FSFSSS, FFFSSS; Y = 7: SSFFS, SFSFSSS, SFFFSSS, FSSFSSS, FSFFSSS, FFSFSSS, FFFFSSS 9. a. Returns to 0 can occur only after an even number of tosses; possible S values are 2, 4, 6, 8, …(i.e. 2(1), 2(2), 2(3), 2(4),…) an infinite sequence, so x is discrete. b. Now a return to 0 is possible after any number of tosses greater than 1, so possible values are 2, 3, 4, 5, … (1+1,1+2, 1+3, 1+4, …, an infinite sequence) and X is discrete 10. a. T = total number of pumps in use at both stations. Possible values: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 b. X: -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6 c. U: 0, 1, 2, 3, 4, 5, 6 d. Z: 0, 1, 2 96
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Chapter 3: Discrete Random Variables and Probability Distributions Section 3.2 11. a. x 4 6 8 P(x) .45 .40 .15 b. 8 7 6 5 4 .50 .40 .30 .20 .10 0 x Relative Frequency c. P(x 6) = .40 + .15 = .55 P(x > 6) = .15 12. a. In order for the flight to accommodate all the ticketed passengers who show up, no more than 50 can show up. We need y 50. P(y 50) = .05 + .10 + .12 + .14 + .25 + .17 = .83 b. Using the information in a. above, P(y > 50) = 1 - P(y 50) = 1 - .83 = .17 c. For you to get on the flight, at most 49 of the ticketed passengers must show up. P(y 49) = .05 + .10 + .12 + .14 + .25 = .66. For the 3 rd person on the standby list, at most 47 of the ticketed passengers must show up. P(y 44) = .05 + .10 + .12 = .27 97
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Chapter 3: Discrete Random Variables and Probability Distributions 13.
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095_Prob and Stat for Eng Soln_Probability and Statistics for Engineering and the Sciences 6TH ED

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