Lecture1

xn n 2 we are interested in the parameter 1

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Unformatted text preview: X 1 , . . . , X n , such that 1.  The Xi’s are independent RV’s; and 2.  Every X i has the same probability distribu$on. We also say that the Xi’s are independently and iden3cally distributed (IID). •  Then the sta$s$c, i.e., a func$on of the X i’s, follows a distribu$on (called sampling distribu3on) that also depends on the unknown parameter θ . We make inference on θ based on the sampling distribu$on. We typically write X 1 , . . . n for hypothe$cal random sample, and the lower , X case x 1 , . . . , x for their observed values. n •  Stat 431 8 Example: Revenue Neutral Tax Bill (Cont’d) •  •  Parameter of interest: average change in tax paid over all tax return forms Sta$s$c: average change in tax paid over the sampled tax return forms •  Sampling distribu$on of the sta$s$c: iid –  Assuming a normal popula$on X1 , . . . , Xn ∼ N (µ, σ 2 ) –  We are interested in the parameter µ ￿ 1 ¯ –  The sta$s$c is X = n Xi –  By STAT 430 knowledge, we know 1 ¯ X ∼ N (µ, n σ 2 ) •  From the observed data: –  Observed average change is  ­$219, with sample SD = $725 ≈ σ •  What do...
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This note was uploaded on 02/25/2013 for the course STAT 431 taught by Professor Stroud during the Spring '08 term at UPenn.

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