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Question
Calculate `"e"_0^circ ,"e"_1^circ , "e"_2^circ` from the following:
| Age x | 0 | 1 | 2 |
| lx | 1000 | 880 | 876 |
| Tx | - | - | 3323 |
Solution
We know that `"e"_"x"^circ = "T"_"x"/"l"_"x"`
| Age x | lx | Lx | Tx |
| 0 | 1000 | 940 | 5141 |
| 1 | 880 | 878 | 4201 |
| 2 | 876 | - | 33236 |
Lx = `("l"_"x" + "l"_("x" + 1))/2` , x = 0,1,2
L0 = `("l"_0 + "l"_1)/2 = (1000 + 880)/2 = 940`
L1 = `("l"_1 + "l"_2)/2 = (880 + 876)/2 = 878`
T2 = 3323 given
T1 = L1 + T2 = 878 + 3323 = 4201
T0 = L0 + T1 = 940 + 4201 = 5141
`"e"_0^circ = "T"_0/"l"_0 = 5141/1000 = 5.141`
`"e"_1^circ = "T"_1/"l"_1 = 4201/880 = 4.7739`
`"e"_2^circ = "T"_2/"l"_2 = 3323/876 = 3.7934`
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