Section A
Q1. The following table shows the initial probability of selection (pi) of the seven units of a population U: {Ui; i = 1, 2, 3, 4, 5, 6, 7}. Let a random sample of size 3 be selected from the population using probability proportional to size without replacement scheme. Let the units selected in the three successive draws be U7, U3 and U5 respectively. Find the selection probabilities with which these units were selected : What are 'Linear Systematic' and 'Circular Systematic' sampling schemes? Under what condition is Linear Systematic sampling scheme applied for selecting a sample of size n from the population of N units? Show that Linear Systematic sampling is also a probability sampling scheme which ensures equal probability of inclusion of each unit of the population in the sample. Explain the processes for analysing an economic problem, being an econometrician following the classical methodology. Illustrate the proceeding steps with Keynesian theory of consumption.
(a)
Population units (Ui)
Label (i)
Initial probability of selection (pi)
(b) What are 'Linear Systematic' and 'Circular Systematic' sampling schemes? Under what condition is Linear Systematic sampling scheme applied for selecting a sample of size n from the population of N units? Show that Linear Systematic sampling is also a probability sampling scheme which ensures equal probability of inclusion of each unit of the population in the sample.
(c) Explain the processes for analysing an economic problem, being an econometrician following the classical methodology. Illustrate the proceeding steps with Keynesian theory of consumption.
