Temple University
Department of Economics
Economics 615
Sampling and Estimation
- (HC) Let X1 and X2 be two draws from the distribution having
p.d.f.
![](Image126.gif)
Find
.
- (HC) Let X have the p.d.f.
.
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.)
(HC) Let X1, X2 be a random sample of size 2 from the distribution
having p.d.f.
.
Let Y1=X1+X2 and Y2=X1/(X1+X2).
Show that Y1 and Y2 are stochastically independent.
(P) Consider the sample values Yt (t=1,2,
,T). Show
![](Image130.gif)
where
and s denote
the realized values of the sample mean and standard deviation respectively.
(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.
(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.
- For what value of
does Y comprise a
random sample?
- Find Var(
) and simplify your answer.
- Is s2 and unbiased estimator of
?
- (P) Let Yt (t=1,2,
T) be a random sample from the p.d.f.
![](Image140.gif)
- Show
is an unbiased estimator for
.
- Find the Cramer-Rao lower bound.