Let Y 1 , Y 2 , Y 3 , and Y 4 be independent, identically distributed random variables from a population with mean and variance 2. Let 11eb9ee2_f03d_c6cf_8edd_b9f01b455e29_SM2712_11 = 11eb9ee2_f03d_c6d0_8edd_25192eecaf26_SM2712_11 (Y 1 +Y 2 + Y 3 + Y 4 ) denote the average of these four random variables. (i) What are the expected value and variance of 11eb9ee2_f03d_c6d1_8edd_978396171fd9_SM2712_11 P in terms of and 2 (ii) Now, consider a different estimator of : W = 11eb9ee2_f03d_c6d2_8edd_19c54b44737c_SM2712_11 Y 1 + 11eb9ee2_f03d_c6d3_8edd_97141ba65d80_SM2712_11 Y 2 + 11eb9ee2_f03d_ede4_8edd_d3e8d5a20d35_SM2712_11 Y 3 + 11eb9ee2_f03d_ede5_8edd_81e60eda7579_SM2712_11 Y 4. This is an example of a weighted average of the Yi. Show that W is also an unbiased estimator of . Find the variance of W. (iii) Based on your answers to parts (i) and (ii), which estimator of do you prefer, 11eb9ee2_f03d_ede6_8edd_7976ab1adbb8_SM2712_11 or W

Introductory Econometrics 4th Edition by Jeffrey Wooldridge

النسخة 4الرقم المعياري الدولي: 978-0324660609

Introductory Econometrics 4th Edition by Jeffrey Wooldridge

النسخة 4الرقم المعياري الدولي: 978-0324660609

تمرين 3

Let Y 1 , Y 2 , Y 3 , and Y 4 be independent, identically distributed random variables from a population with mean and variance 2. Let

(Y 1 +Y 2 + Y 3 + Y 4 ) denote the average of these four random variables.
(i) What are the expected value and variance of

P in terms of and 2
(ii) Now, consider a different estimator of :
W =

Y 1 +

Y 2 +

Y 3 +

Y 4.
This is an example of a weighted average of the Yi. Show that W is also an unbiased estimator of . Find the variance of W.
(iii) Based on your answers to parts (i) and (ii), which estimator of do you prefer,

or W

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موثّق

The following variables are random and i...