Ch8 Test Bank

b. The likelihood for any individual estimation of a constant irregular variable is zero, yet for discrete arbitrary factors it isn't. c. Likelihood for constant arbitrary factors implies finding the zone under a bend, while for discrete irregular factors it implies adding singular probabilities. d. These decisions are valid. ANS:DPTS:1REF:SECTION 8. 1 2. Which of coming up next is in every case valid for all likelihood thickness elements of consistent irregular factors? a. The likelihood at any single point is zero. b. They contain an uncountable number of potential qualities. c. The absolute region under the thickness work f(x) approaches 1. d. These decisions are valid. ANS:DPTS:1REF:SECTION 8. 1 3. Assume f(x) = 0. 25. What scope of potential qualities would x be able to take on and still have the thickness work be real? a. [0, 4] b. [4, 8] c. [? 2, +2] d. These decisions are valid. ANS:DPTS:1REF:SECTION 8. 1 4. The likelihood thickness work, f(x), for any consistent irregular variable X, speaks to: a. ll potential qualities that X will accept inside some stretch a ? x ? b. b. the likelihood that X takes on a particular worth x. c. the stature of the thickness work at x. d. None of these decisions. ANS:CPTS:1REF:SECTION 8. 1 5. Which of coming up next is valid about f(x) when X has a uniform appropriation over the span [a, b]? a. The estimations of f(x) are diverse for different estimations of the irregular variable X. b. f(x) rises to one for every conceivable estimation of X. c. f(x) rises to one separated by the length of the stretch from a to b. d. None of these decisions. ANS:CPTS:1REF:SECTION 8. 1 6. The likelihood thickness work f(x) for a uniform arbitrary variable X characterized over the span [2, 10] is a. 0. 125 b. 8 c. 6 d. None of these decisions. ANS:APTS:1REF:SECTION 8. 1 7. On the off chance that the arbitrary variable X has a uniform dispersion somewhere in the range of 40 and 50, at that point P(35 ? X ? 45) is: a. 1. 0 b. 0. 5 c. 0. 1 d. unclear. ANS:BPTS:1REF:SECTION 8. 1 8. The likelihood thickness work f(x) of an arbitrary variable X that has a uniform conveyance among an and b is a. (b + a)/2 b. 1/b ? 1/a c. (a ? b)/2 d. None of these decisions. ANS:DPTS:1REF:SECTION 8. 1 9. Which of the accompanying doesn't speak to a constant uniform arbitrary variable? . f(x) = 1/2 for x between ? 1 and 1, comprehensive. b. f(x) = 10 for x somewhere in the range of 0 and 1/10, comprehensive. c. f(x) = 1/3 for x = 4, 5, 6. d. None of these decisions speaks to a ceaseless uniform arbitrary variable. ANS:CPTS:1REF:SECTION 8. 1 10. Assume f(x) = 1/4 over the range a ? x ? b, and a ssume P(X 4) = 1/2. What are the qualities for an and b? a. 0 and 4 b. 2 and 6 c. Can be any scope of x esteems whose length (b ? an) approaches 4. d. Can't reply with the data given. ANS:BPTS:1REF:SECTION 8. 1 11. What is the state of the likelihood thickness work for a uniform arbitrary variable on the stretch [a, b]? a. A square shape whose X esteems go from a to b. b. A straight line whose stature is 1/(b ? an) over the range [a, b]. c. A constant likelihood thickness work with a similar estimation of f(x) from a to b. d. These decisions are valid. ANS:DPTS:1REF:SECTION 8. 1 TRUE/FALSE 12. A persistent likelihood dispersion speaks to an arbitrary variable having an interminable number of results which may expect any number of qualities inside a stretch. ANS:TPTS:1REF:SECTION 8. 1 13. Consistent likelihood disseminations depict probabilities related with irregular factors that can accept any limited number of qualities along a span. ANS:FPTS:1REF:SECTION 8. 1 14. A ceaseless irregular variable is one that can expect an uncountable number of qualities. ANS:TPTS:1REF:SECTION 8. 1 15. Since there is an unbounded number of qualities a ceaseless arbitrary variable can accept, the likelihood of every individual worth is for all intents and purposes 0. ANS:TPTS:1REF:SECTION 8. 1 16. A ceaseless irregular variable X has a uniform appropriation somewhere in the range of 10 and 20 (comprehensive), at that point the likelihood that X falls somewhere in the range of 12 and 15 is 0. 30. ANS:TPTS:1REF:SECTION 8. 1 17. A ceaseless arbitrary variable X has a uniform circulation somewhere in the range of 5 and 15 (comprehensive), at that point the likelihood that X falls somewhere in the range of 10 and 20 is 1. . ANS:FPTS:1REF:SECTION 8. 1 18. A consistent arbitrary variable X has a uniform dissemination somewhere in the range of 5 and 25 (comprehensive), at that point P(X = 15) = 0. 05. ANS:FPTS:1REF:SECTION 8. 1 19. We recogn ize discrete and ceaseless irregular factors by noticing whether the quantity of potential qualities is countable or uncountable. ANS:TPTS:1REF:SECTION 8. 1 20. Practically speaking, we as often as possible utilize a consistent circulation to estimated a discrete one when the quantity of qualities the variable can accept that is countable however huge. ANS:TPTS:1REF:SECTION 8. 1 21. Let X speak to week by week salary communicated in dollars. Since there is no set maximum breaking point, we can't recognize (and in this way can't check) all the potential qualities. Thusly, week by week pay is viewed as a ceaseless irregular variable. ANS:TPTS:1REF:SECTION 8. 1 22. To be a real likelihood thickness work, every conceivable estimation of f(x) must be non-negative. ANS:TPTS:1REF:SECTION 8. 1 23. To be a real likelihood thickness work, every conceivable estimation of f(x) must lie somewhere in the range of 0 and 1 (comprehensive). ANS:FPTS:1REF:SECTION 8. 1 24. The aggregate of all estimations of f(x) over the scope of [a, b] must rise to one. ANS:FPTS:1REF:SECTION 8. 1 25. A likelihood thickness work shows the likelihood for each estimation of X. ANS:FPTS:1REF:SECTION 8. 1 26. In the event that X is a persistent irregular variable on the stretch [0, 10], at that point P(X 5) = P(X ? 5). ANS:TPTS:1REF:SECTION 8. 1 27. In the event that X is a consistent arbitrary variable on the stretch [0, 10], at that point P(X = 5) = f(5) = 1/10. ANS:FPTS:1REF:SECTION 8. 1 28. On the off chance that a point y lies outside the scope of the potential estimations of an arbitrary variable X, at that point f(y) must approach zero. ANS:TPTS:1REF:SECTION 8. 1 COMPLETION 29. A(n) ____________________ irregular variable is one that expect an uncountable number of potential qualities. ANS:continuous PTS:1REF:SECTION 8. 1 30. For a persistent irregular variable, the likelihood for every individual estimation of X is ____________________. ANS: zero 0 PTS:1REF:SECTION 8. 1 31. Likelihood for constant irregular factors is found by finding the ____________________ under a bend. ANS:area PTS:1REF:SECTION 8. 1 32. A(n) ____________________ arbitrary variable has a thickness work that appears as though a square shape and you can utilize regions of a square shape to discover probabilities for it. ANS:uniform PTS:1REF:SECTION 8. 1 33. Assume X is a persistent irregular variable for X among an and b. At that point its likelihood ____________________ work must non-negative for all estimations of X among an and b. ANS:density PTS:1REF:SECTION 8. 1 34. The absolute territory under f(x) for a consistent arbitrary variable must rise to ____________________. ANS: 1 one PTS:1REF:SECTION 8. 1 35. The likelihood thickness capacity of a uniform irregular variable on the stretch [0, 5] must be ____________________ for 0 ? x ? 5. ANS: 1/5 0. 20 PTS:1REF:SECTION 8. 1 36. To discover the likelihood for a uniform arbitrary variable you take the ____________________ times the ____________________ of its relating square shape. ANS: base; tallness stature; base length; width; length PTS:1REF:SECTION 8. 1 37. You can utilize a consistent arbitrary variable to ____________________ a discrete irregular variable that takes on a countable, yet extremely huge, number of potential qualities. ANS:approximate PTS:1REF:SECTION 8. 1 SHORT ANSWER 38. A nonstop arbitrary variable X has the accompanying likelihood thickness work: f(x) = 1/4, 0 ? x ? 4 Find the accompanying probabilities: a. P(X ? 1) b. P(X ? 2) c. P(1 ? X ? 2) d. P(X = 3) ANS: a. 0. 25 b. 0. 50 c. 0. 25 d. 0 PTS:1REF:SECTION 8. 1 Waiting Time The period of time patients must stand by to see a specialist at a crisis room in an enormous clinic has a uniform conveyance between 40 minutes and 3 hours. 39. {Waiting Time Narrative} What is the likelihood thickness work for this uniform circulation? ANS: f(x) = 1/140, 40 ? x ? 180 (minutes) PTS:1REF:SECTION 8. 1 40. {Waiting Time Narrative} What is the likelihood that a patient would need to hold up somewhere in the range of one and two hours? ANS: 0. 43 PTS:1REF:SECTION 8. 1 41. {Waiting Time Narrative} What is the likelihood that a patient would need to stand by precisely 60 minutes? ANS: 0 PTS:1REF:SECTION 8. 1 42. {Waiting Time Narrative} What is the likelihood that a patient would need to stand by close to 60 minutes? ANS: 0. 143 PTS:1REF:SECTION 8. 1 43. The time required to finish a specific gathering activity has a uniform dispersion somewhere in the range of 25 and 50 minutes. a. What is the likelihood thickness work for this uniform dispersion? b. What is the likelihood that the get together activity will require over 40 minutes to finish? c. Assume additional time was permitted to finish the activity, and the estimations of X were stretched out to the range from 25 to an hour. What might f(x) be for this situation? ANS: a. f(x) = 1/25, 25 ? x ? 50 b. 0. 40 c. f(x) = 1/35, 25 ? x ? 60 PTS:1REF:SECTION 8. 1 44. Assume f(x) rises to 1/50 on the span [0, 50]. a. What is the dispersion of X? b. What does the diagram of f(x) resemble? c. Discover P(X ? 25) d. Discover P(X ? 25) e. Discover P(X = 25) f. Discover P(0 X 3) g. Discover P(? 3 X 0) h. Discover P(0 X 50) ANS: a. X has a uniform conveyance on the span [0, 50]. b. f(x) structures a square shape of tallness 1/50 from x = 0 to x = 50. c. 0. 50 d. 0. 50 e. 0 f. 0. 06 g. 0. 06 h. 1. 00 PTS:1REF:SECTION 8. 1 Chemistry Test The time it takes an understudy to complete a science test has a uniform conveyance somewhere in the range of 50 and 70 minutes. 45. {Chemistry Test Narrative} What is the likelihood thickness work for this uniform appropriation? ANS: f(x) = 1/20, 50 ? x ? 70 PTS:1REF:SECTION 8. 1 46. {Chemistry Test Narrative} Find the likelihood that an understudy will take over an hour to complete the test. ANS: 0. 50 PTS:1REF:SECTION 8. 1 47. {Chemistry Test Narrative} Find the likelihood that an understudy will take no under 55 minutes to complete the test. ANS: 0. 75 PTS:1REF:SECTION 8. 1 48. {Chemistry Test Narrativ