Estimate probable life expectation of life of an average Indian at the

1.	Estimate probable life expectation of life of an average Indian at the ages 25 and 40.
Answer» Since the known values are 5, the estimation is based on the expansion of Δ⁵ = (y – 1)⁵= 0 ∴ Δ⁵= (y – 1)⁵ = y₅ – 5y₄ + 10y₃ – 10y₂ + 5y₁ – y₀ = 0 We have to determine the value of y_3; 20.1 – 5(23.1) + 10y₃ – 10(29.1) + 5(32.2) – 35.4 = 0 So, by simplifying, 10y₃ – 260.8 = 0 ∴ y₃ = 26.08 years Hence, the probable expectation of life at the age 25 is 26.08 years. Now expand (y – 1)⁵ = 0 with change of subscript, keeping coefficients as it is. y₆ – 5y₅ + 10y₄ – 10y₃ + 5y₂ – y₁ = 0 y₆ – 5(20.1) + 10(23.1) – 10(26.08) + 5(29.1)-32.2 = 0 y₆– 17 = 0, y₆= 17 years.

Estimate probable life expectation of life of an average Indian at the ages 25 and 40.

Answer»

Since the known values are 5, the estimation is based on the expansion of Δ⁵

= (y – 1)⁵= 0

∴ Δ⁵= (y – 1)⁵

= y₅ – 5y₄ + 10y₃ – 10y₂ + 5y₁ – y₀ = 0

We have to determine the value of y_3;

20.1 – 5(23.1) + 10y₃ – 10(29.1) + 5(32.2) – 35.4 = 0

So, by simplifying, 10y₃ – 260.8 = 0

∴ y₃ = 26.08 years

Hence, the probable expectation of life at the age 25 is 26.08 years.

Now expand (y – 1)⁵ = 0 with change of subscript, keeping coefficients as it is.

y₆ – 5y₅ + 10y₄ – 10y₃ + 5y₂ – y₁ = 0

y₆ – 5(20.1) + 10(23.1) – 10(26.08) + 5(29.1)-32.2 = 0

y₆– 17 = 0, y₆= 17 years.