Demography Assignment 1

INDIAN STATISTICAL INSTITUTE

Assignment B. STAT, II YEAR Demography Date of Circulation: 23rd March, 2007 Last date of submission: 5th April, 2007

Maximum marks: 10

Answer the following questions. 1) Construct the values of ei0 from the relation l i =

l0 for i = 0,1,...,6 and l 7 = 0. Exp(i )

[Note: Choose the numerical value of l 0 as 1000] (4.5 Marks)

2) In the year 2005, there were 3000 live births and 460 infant deaths recorded in a village. In the proceeding year, the number of live births remained the same as the previous year, but infant deaths reduced to half of the previous year’s number. It was estimated that 60 per cent of the infant deaths in 2005 were from the same year’s birth cohort. This percentage remained the same for the proceeding year’s infant deaths. None of the infant deaths recorded in the year 2007 were from previous year’s birth cohort. The number of live births and infant deaths in 2004 were 3100 and 500 respectively. Find the probability of the infant mortality in 2006. (2.5 Marks) ω−x

∫ t.l ( x + t ) µ ( x + t )dt

ω−x

3) If Tx =

∫ l ( x + t )dt , 0

then the expression

0

ω−x

represents which

∫ l ( x + t ) µ ( x + t )dt 0

column of the life table? Prove. [Everyone among l0 dies before age ω ] (3 Marks)