Temple University

Department of Economics

Economics 615

Sampling and Estimation

 

  1. (HC) Let X1 and X2 be two draws from the distribution having p.d.f.

    2. Find .

     

  2. (HC) Let X have the p.d.f.

    3. .

    Find the p.d.f. of the random variable Y=2X+1. (Hint: This is a one to one transformation of random variables of the discrete type.)

  3. (HC) Let X1, X2 be a random sample of size 2 from the distribution having p.d.f. .

    4. Let Y1=X1+X2 and Y2=X1/(X1+X2). Show that Y1 and Y2 are stochastically independent.

  4. (P) Consider the sample values Yt (t=1,2,…,T). Show

    5. where and s denote the realized values of the sample mean and standard deviation respectively.

  5. (P) Consider a random sample Yt (t=1,2,…T) from a population. Find the minimum value of T such that the probability is .95 that the sample mean will not differ from the population mean by more than 25 percent of the standard deviation.
  6. (P) Suppose Y=[y1, Y2,…YT]' where , is a Tx1 vector with each element equal to unity, and is a scalar such that is positive definite.
  1. For what value of does Y comprise a random sample?
  2. Find Var() and simplify your answer.
  3. Is s2 and unbiased estimator of ?
  1. (P) Let Yt (t=1,2,…T) be a random sample from the p.d.f.

  1. Show is an unbiased estimator for .
  2. Find the Cramer-Rao lower bound.