9- ehtimolliklar nazariyasining limit teoremalari

O’z-o’zini tekshirish uchun savollar

1. 
   Chebishev tengsizligini yozing.
   
2. 
   Chebishev teoremasini aytib bering.
   
3. 
   Markaziy limit teoremasini aytib bering.
   

Mustaqil yechish uchun mashqlar

Normal taqsimlangan X tasodifiy miqdor matematik kutilishi a ga, o’rtacha kvadratik chetlanishi σ ga teng. Uning (α, β) intervaldan qiymat qabul qilish ehtimolligini toping.

41. a=18, σ=5, =13, =33.
42. a=5, σ=1, =4, =6.
43. a=9, σ=5, =4, =24.
44. a=18, σ=4, =14, =24.
45. a=12, σ=3, =9, =15.
46. a=16, σ=5, =13, =21.
47. a=10, σ=2, =6, =16.
48. a=11, σ=6, =4, =24.
49. a=3, σ=2, =0, =9.
50. a=8, σ=5, =3, =20.
51. a=6, σ=1, =5, =7.

52. Kungaboqar urug’ining og’irligi normal taqsimlangan tasodifiy miqdor bo’lsin. Uning matematik kutilishi a=58 mg va o’rtacha kvadratik chetlanishi σ=1 bo’lsa, tasodifiy olingan urug’ og’irligi 57 mg. dan 60 mgrammgacha bo’lish ehtimolligini toping.

X tasodifiy miqdor normal taqsimlangan bo’lib, o’rtacha kvadratik chetlanishi σ ma’lum bo’lsa, lX-al<δ tengsizlik bajarilishi ehtimolligini toping.
53. a=14, σ=3, δ=5.

54. a=13, σ=4, δ=9.

55. a=12, σ=5, δ=3.

56. a=2, σ=2, δ=4.

57. a=11, σ=7, δ=11.