Problem%20Set%2004_2010_2011[1]

# Problem%20Set%2004_2010_2011[1] - Middle East Technical...

This preview shows pages 1–3. Sign up to view the full content.

ECON 206 1 Middle East Technical University 2010-2011 Fall Department of Economics ECON 206 Instructor: Ozan ERUYGUR Research Assistant: Pelin AKÇAGÜN PROBLEM SET 04 ESTIMATION – UNBIASEDNESS – MSE – CONFIDENCE INTERVALS PROBLEM 1 Suppose that   12 ˆˆ EE   ,   2 11 ˆ V and   2 22 ˆ V . Consider the estimator  31 2 ˆ 1 aa  . a) Show that 3 ˆ is an unbiased estimator for . b) If 1 ˆ and 2 ˆ are independent how should be constant a be chosen in order to minimize the variance of 3 ˆ ? PROBLEM 2 Suppose that , 3 , YYY denote a random sample from an exponential distribution with density function / 1 ,0 0, y ey fy elsewhere    . Consider the following estimators of : ˆ Y , 2 ˆ 2 YY , 3 2 ˆ 3 ,   41 2 3 ˆ min , , , 5 ˆ Y . a) Which of these estimators are unbiased? b) Among the unbiased estimators, which has the smallest variance? PROBLEM 3 The reading on a voltage meter connected to a test circuit is uniformly distributed over the interval ,1 , where is the true but unknown voltage of the circuit. Suppose that , , ..., n Y denotes a random sample of such readings. a) Show that Y is a biased estimator of , and compute the bias. b) Find a function of Y that is an unbiased estimator of . c) Find   MSE Y when Y is used as an estimator of .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
ECON 206 2 PROBLEM 4 An increase in the rate of consumer savings frequently is tied to a lack of confidence in the economy and is said to be an indicator of a recessional tendency in the economy. A random sampling of n = 200 savings accounts in a local community showed the mean increase in savings account values to be 7.2% over the past 12 months, with standard deviation 5.6%. Estimate the mean percentage increase in savings account values over the past 12 months for depositors in the community.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 4

Problem%20Set%2004_2010_2011[1] - Middle East Technical...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online