Question: please solve quickly Q.1(a) Show that S ST M-m M is unbiased estimator for $; for Two stage sampling. (9+6) (b) Argue how one stage

please solve quickly

Q.1(a) Show that S ST M-m M is unbiased estimator for $; for Two stage sampling. (9+6) (b) Argue how one stage sampling is less advantageous in comparison to Two stage sampling. Q.2(a) Drive expression for unbiased estimate of variance in case sample of n units is drawn with probability proportional to size say k;- (8+7) (b) Describe the two procedures for selecting samples when size of cluster varies using numerical examples. Q.3:(a) Show that an unbiased estimate of V(f) in two stage sampling where N are first stage units and M, are second stage units is given by: V(t) = N - (7+8) (b) Prove that stratified random sampling is more precise than other probability sampling techniques in case population is linear in trend

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