P2
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Dificultate scazuta 1. complementare 2. F 3. A 4. F 5. F 6. A 7. A 8. A 9. A 10. F 11. F 12. A 13. A 14. imposibil 15. elementar 16. compus 17. reuniunea 18. intersectia 19. incompatibile 20. sigur 21. imposibil 22. discreta 23. independente 24. A 25. A 26. A 27. F 28. F Dificultate medie 1. 11 2. 22 3. x 3 = 21, p 3 = 0,2 4. x 3 = 25, p 3 = 0,4 5. p 1 = 0,4; p 2 = 0,1; p 3 = 0,5 6. m ≤ M ≤ M(X) 7.
8.
9.
10. 69 11. 74 12.
13.
14. F 15. F 16 A 17. p﴾│X-M(X)│<3σ﴿ ≥8 9 18. p﴾│X-M(X)│<0,2﴿≥0,9 19. ε= 0,3 20. p﴾│X-M(X)│<0,2﴿≥0,64 21. p﴾│X-M(X)│<√0,4﴿≥0,909 22.
23.
24.
25.
0, x ≤ 0 F(x) = sin x,0 < x ≤ π / 2 1, x > π / 2 0, x ≤ 0 1 2 F(x)= ( x − x),0 < x ≤ 2 2 1, x > 2
26.
27.
28. 29 30
0, x ≤ 0 F(X) = 1 − cos x,0 < x ≤ π / 2 1, x > π / 2 M(X)= 2 3 M(X) = 4 3
31 32 33 34 35 36 37
38 39 40 41 42 43 44
0, x ≤ 0 1 f(x) = ,0 < x ≤ 4 4 0, x > 4
M(X) = 1 D 2 (X) = 4 3 M(X) = 2,2 M(X 2 ) = 5,8 M(X) = 3,9 0, x ≤ 2 0,5,2 < x ≤ 4 F(X)= 0,7,4 < x ≤ 7 1, x > 7 0, x ≤ 2 0,1,2 < x ≤ 3 F(X)= 0,5,4 < x ≤ 5 1, x > 5 M(X)=3,5 M(X 2 ) = 16,5 M(X 2 ) = 13,3 D(X 2 ) = 1,05 M(X 3 )=74,1
45.
1. 2. 3. 4. 5.
46. P(X<3)=0,5 47. Toate variantele a);b);c). (Evenimentul contrar lui A, evenimentul complementar lui A, evenimentul opus lui A) 48. Incompatibile 49. E 1C va fi : bila extrasa nu este alba 50. Nici o varianta nu este corecta 51. 0,89 52. 0,78 53. 0,5 54. ~0,804 55. ~0,391 Dificultate ridicata 1 A A A
6. 7. A
8. A 9. A 10. A 11. A 12. A 13. A 14. A 15. A 16. A 17. A 18. A 19. A 20. A 21. A 22. F 23. F 24. F 25. F 26. F 27. F 28. F 29. F 30. F 31.
32.
33.
34.
35.
36.
37. 1 2 3
a=π 2 2arctg(e2x) π 2arctg(e) – 1 π
38.
1
2 3 4 5
0 4/3 4/3 1/2
39. 1
2
3
40.
1 12/7 2
3
41. 42. 43. 44. 45. 46. 47. 48. 49.
1 5/6 2 7/24 3 5/32 A 2 15 29 60 0 -3 -11 ∞ 1
2
50. 2
51. 52. 53.
2x﴾x+1﴿ ﴾ 3﴿ 5 6
8.
9.
10. 69 11. 74 12.
13.
14. F 15. F 16 A 17. p﴾│X-M(X)│<3σ﴿ ≥8 9 18. p﴾│X-M(X)│<0,2﴿≥0,9 19. ε= 0,3 20. p﴾│X-M(X)│<0,2﴿≥0,64 21. p﴾│X-M(X)│<√0,4﴿≥0,909 22.
23.
24.
25.
0, x ≤ 0 F(x) = sin x,0 < x ≤ π / 2 1, x > π / 2 0, x ≤ 0 1 2 F(x)= ( x − x),0 < x ≤ 2 2 1, x > 2
26.
27.
28. 29 30
0, x ≤ 0 F(X) = 1 − cos x,0 < x ≤ π / 2 1, x > π / 2 M(X)= 2 3 M(X) = 4 3
31 32 33 34 35 36 37
38 39 40 41 42 43 44
0, x ≤ 0 1 f(x) = ,0 < x ≤ 4 4 0, x > 4
M(X) = 1 D 2 (X) = 4 3 M(X) = 2,2 M(X 2 ) = 5,8 M(X) = 3,9 0, x ≤ 2 0,5,2 < x ≤ 4 F(X)= 0,7,4 < x ≤ 7 1, x > 7 0, x ≤ 2 0,1,2 < x ≤ 3 F(X)= 0,5,4 < x ≤ 5 1, x > 5 M(X)=3,5 M(X 2 ) = 16,5 M(X 2 ) = 13,3 D(X 2 ) = 1,05 M(X 3 )=74,1
45.
1. 2. 3. 4. 5.
46. P(X<3)=0,5 47. Toate variantele a);b);c). (Evenimentul contrar lui A, evenimentul complementar lui A, evenimentul opus lui A) 48. Incompatibile 49. E 1C va fi : bila extrasa nu este alba 50. Nici o varianta nu este corecta 51. 0,89 52. 0,78 53. 0,5 54. ~0,804 55. ~0,391 Dificultate ridicata 1 A A A
6. 7. A
8. A 9. A 10. A 11. A 12. A 13. A 14. A 15. A 16. A 17. A 18. A 19. A 20. A 21. A 22. F 23. F 24. F 25. F 26. F 27. F 28. F 29. F 30. F 31.
32.
33.
34.
35.
36.
37. 1 2 3
a=π 2 2arctg(e2x) π 2arctg(e) – 1 π
38.
1
2 3 4 5
0 4/3 4/3 1/2
39. 1
2
3
40.
1 12/7 2
3
41. 42. 43. 44. 45. 46. 47. 48. 49.
1 5/6 2 7/24 3 5/32 A 2 15 29 60 0 -3 -11 ∞ 1
2
50. 2
51. 52. 53.
2x﴾x+1﴿ ﴾ 3﴿ 5 6
