Chapter3 - 95 CHAPTER 3 Section 3.1 1 S FFF SFF FSF FFS FSS...

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Unformatted text preview: 95 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 Chapter 3: Discrete Random Variables and Probability Distributions 96 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 Chapter 3: Discrete Random Variables and Probability Distributions 97 Section 3.2 11....
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This note was uploaded on 03/30/2008 for the course STAT 211 taught by Professor Parzen during the Spring '07 term at Texas A&M.

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Chapter3 - 95 CHAPTER 3 Section 3.1 1 S FFF SFF FSF FFS FSS...

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