Life Tables and Probabilities — Transcript

Full transcript

1. 0:03uh hi everyone in this video we'll talk
2. 0:04about the life tables and the
3. 0:07probabilities uh so in Insurance
4. 0:09business the probability for survival is
5. 0:12a important concept uh so how do you
6. 0:15define the probability for survival so
7. 0:18suppose uh um if we write it in this way
8. 0:22the p uh
9. 0:24X1 that means that a person uh age uh is
10. 0:30equal to X and we are calculating the
11. 0:32probability to survive probability to
12. 0:38survive uh for uh 1
13. 0:42year so this is how this notation uh can
14. 0:46be seen and same way if we have
15. 0:49qx1 that that means that person is still
16. 0:52age X and uh what is a
17. 0:56probability uh uh for the dying so how
18. 1:02what's the probability that the person
19. 1:03will die so in that case if you look at
20. 1:06this notation this notation should be
21. 1:08equal to 1 - qx1 so this is how uh we
22. 1:13use the notations uh for probability to
23. 1:16survive and probability to die and uh so
24. 1:20we have more notations so suppose if we
25. 1:22write it this way um
26. 1:27qx1 2 so this means that the person his
27. 1:32age uh is X and we want to calculate the
28. 1:36probability that he
29. 1:41survive uh for 2
30. 1:43years and then
31. 1:46die uh in third
32. 1:50year so this is how uh we call it uh we
33. 1:55we look at this notation so how one will
34. 1:58calculate this uh this can be calculated
35. 2:01as uh Q of
36. 2:04X1 2 uh is equal to probability of x to
37. 2:10survive uh 2 years and then uh
38. 2:14probability to die so that will be equal
39. 2:17to 1 minus probability of x
40. 2:22+ uh 2 and one so this is how you can
41. 2:27calculate or you can also write it this
42. 2:29way probability to survive for 2 years
43. 2:33and probability to
44. 2:35die
45. 2:36uh within 1 year after you are x + 2
46. 2:40year old so this is how you can uh look
47. 2:43at this uh
48. 2:46formula now uh life tables so sometimes
49. 2:51we are given life tables so this is uh
50. 2:54this has following columns age and
51. 2:58suppose the age starts from 7
52. 3:0071 72 73 and we have uh numbers numbers
53. 3:07will be like 100 90 70 and 50 so what
54. 3:13does it mean it means that suppose if we
55. 3:16start with 100 people at 870 then uh
56. 3:19there will be only 90 people
57. 3:22871 and only 70 at AG 72 and only 50 at
58. 3:27ag8 73 so that means people
59. 3:30died and uh the number of Deads will be
60. 3:3410 at
61. 3:35870 uh will be 20 at 871 and will be 20
62. 3:41at 872 right so how one can get these
63. 3:45numbers so mostly we uh have uh count
64. 3:50for the population so city has this data
65. 3:53and they can um uh estimate how many
66. 3:56people are at particular ages and what
67. 3:59are their uh survival times and based on
68. 4:04this data uh because this we are looking
69. 4:07at a huge population we can get an
70. 4:09overall estimate of what's the normal
71. 4:12trend for people to survive at what age
72. 4:15it's more probable for them to die so
73. 4:17how do we use uh this for this uh table
74. 4:20so suppose uh if you want to calculate
75. 4:23probability for age 70 uh to survive for
76. 4:272 years so how we do this is
77. 4:30so as we can see there are 100 people at
78. 4:33age 70 and after 2 years there are only
79. 4:3670% left so therefore the probability to
80. 4:39survive is7 so that will be our answer
81. 4:44and if we say what's the probability for
82. 4:47someone um at age 72 to survive for one
83. 4:51year and in that case we look at 72 so
84. 4:54there are 70 people and for them to
85. 4:57survive to age 73 uh we have to divide
86. 5:00it by 50 and so because there are only
87. 5:0350 people uh at that time so that will
88. 5:06be our answer if you want to calculate
89. 5:10what's
90. 5:11the uh probability for age uh
91. 5:16uh 72 to die within one year in that
92. 5:20case it will be equal to 20 by
93. 5:2370 so again if you want to calculate how
94. 5:27to uh
95. 5:30like suppose if we say Q 70 and uh say 1
96. 5:36and two so the person has to survive for
97. 5:382 years and then die in the third year
98. 5:41in that case uh it will be equal
99. 5:45to
100. 5:49um 20 / 100 because the person uh can
101. 5:55die
102. 5:57um the probability for person to die
103. 6:00uh in the third year will be uh 20% and
104. 6:03then he has to survive for uh that time
105. 6:07so that survival will be given by
106. 6:11um
107. 6:1370 by 100 so that will be our
108. 6:18probability so I hope this tutorial help
109. 6:20and I'll see you again with more
110. 6:22Concepts thank
111. 6:28you