Math Solutions

(Solution Library) Let Y 1 , Y 2 , Y 3 , and Y 4 be independent random variables with means  1 ,  2 ,  3 ,  4 , and equal variance  2 . For each of the

Question: Let Y 1 , Y 2 , Y 3 , and Y 4 be independent random variables with means  1 ,  2 ,  3 ,  4 , and equal variance  2 . For each of the following linear combinations of these Y’s determine the coefficients c 1 , c 2 , c 3 , c 4 in the general formula Z = c 1 Y 1 + c 2 Y 2 + c 3 Y 3 + c 4 Y 4 .

  1. Z 1 = Y 1 + Y 2 .
  2. Z 2 = Y 1 - Y 2 .
  3. Z 3 = (Y 1 + Y 2 )/2 - (Y 3 + Y 4 )/2
  4. Z 4 = (Y 1 - Y 2 )/2 - (Y 3 - Y 4 )/2
  5. Z 5 = Y 1 - (Y 2 + Y 3 + Y 4 )/3

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