hw10sol - Econ 3190 Fall 2011 HW10 Solution 1#8.14 Suppose...

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Econ 3190 Fall 2011 HW10 Solution 1. #8.14 Suppose S 2 n = 1 n 1 n X i =1 ( X i X ) 2 Now we have Y i = X i + c Y = 1 n n X i =1 Y i = 1 n n X i =1 ( X i + c ) = c + 1 n n X i =1 X i = c + X b S 2 n = 1 n 1 n X i =1 ( Y i Y ) 2 = 1 n 1 n X i =1 ( X i + c ( c + X )) 2 = 1 n 1 n X i =1 ( X i X ) 2 = S 2 n As such, sample variance is unchanged if a constant c is added to or substracted from each observation. Now, we have Y i = cX i Y = 1 n n X i =1 Y i = 1 n n X i =1 ( cX i ) = c 1 n n X i =1 X i = c X 1
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S 2 n = 1 n 1 n X i =1 ( Y i Y ) 2 = 1 n 1 n X i =1 ( cX i c X ) 2 = c 2 1 n 1 n X i =1 ( X i X ) 2 = c 2 S 2 n As such, we showed the sample variance becomes c 2 times its original value if we each observation is multiplied by c: 2. #8.23 P ( X < 5 : 5) = P ( z < 5 : 5 5 : 3 0 : 9 = p 6 ) = P ( z < 1 : 33) = 0 : 9082 3. #8.26 (a) P ( X < 2 : 7) = P ( z < 2 : 7 3 : 2 1 : 6 = 8 ) = P ( z < 2 : 5) = 0 : 0062 (b) P ( X > 3 : 5) = P ( z > 3 : 5 3 : 2 1 : 6 = 8
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This note was uploaded on 11/30/2011 for the course ECON 3190 at Cornell.

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hw10sol - Econ 3190 Fall 2011 HW10 Solution 1#8.14 Suppose...

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