Section A
Q1.
(a) Describe the advantages of sampling versus complete enumeration. Write the circumstances under which complete enumeration is preferred to sampling.
(b) In the regression model yi = α + β xi + ui, i = 1, 2, ..., n, if the sample mean \barx of x is zero, show that cov(\hatα, \hatβ) = 0, where \hatα and \hatβ are the least square estimators of α and β. Assume that u1, u2, \dots, un are independent and are from N(0, σ^2) distribution.
(c) Define stationary time series process and autocovariance function. Show that autocovariance function, denoted by γ(h), is an even function, positive semi-definite and uniformly continuous if it is continuous at h = 0.
