231hw1solutionsF11

231hw1solutionsF11 - Will Landau STAT 231 Problem Set 1...

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Unformatted text preview: Will Landau August 18, 2011 STAT 231 Problem Set 1 Solutions Exercise 1.1 (Devore 1.42) . a. Suppose our sample of x i ’s is { x 1 ,...,x n } for some n . The sample has mean x and median e x . Then: y = ∑ n i =1 y i n = ∑ n i =1 x i + c n = ∑ n i =1 x i n + nc n = x + c If n is odd, then: e y = y n +1 2 = x n +1 2 + c = e x + c If n is even, then the answer is the same: e y = y n 2 + y ( n 2 +1) 2 = x n 2 + c + x ( n 2 +1) + c 2 = x n 2 + x ( n 2 +1) 2 + c + c 2 = e x + c If our sample of x i ’s is { 2 , 3 , 3 , 4 , 5 } , then x = 3 . 4 and e x = 3. If c = 3, then y = 6 . 4 and e y = 6. If c = 7, then y = 10 . 4 and e y = 10. b. y = ∑ n i =1 y i n = ∑ n i =1 cx i n = c ∑ n i =1 x i n = c x If n is odd, then: e y = y n +1 2 = c · x n +1 2 = c e x If n is even, then the answer is the same: e y = y n 2 + y ( n 2 +1) 2 = c · x n 2 + c · x ( n 2 +1) 2 = c · x n 2 + x ( n 2 +1) 2 = c e x If our sample of x i ’s is { 2 , 3 , 3 , 4 , 5 } , then x = 3 . 4 and e x = 3. If c...
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This note was uploaded on 02/11/2012 for the course STAT 231 taught by Professor Staff during the Fall '08 term at Iowa State.

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231hw1solutionsF11 - Will Landau STAT 231 Problem Set 1...

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