MA2222_Notes

MA2222_Notes - The Chebyshev Inequality {I . 4 {3 $ $ The...

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Unformatted text preview: The Chebyshev Inequality {I . 4 {3 $ $ The Chebyshev Inequality for I {I{ IJ{I{ How to estimate ? {I . I- {4 $ {I . {4 {4 $ . . {I . 4 { 3 {I . I Let I $ $ I . 4 I . . $ J F4 J F3 $ . How is $ { #{ $ distributed? $ has Central Limit Theorem I Normal Distribution ) J $ when (J 4 has { Normal Distribution for I I has (# $ {J . {. (# I . {I{ J , IJ{I{ { I has { {. {I 3 { { {, . $ has {J{. Parameter . . . $ Confidence Intervals Assumptions $ { { or J large $ known $ { { $ unknown $ {, { $ {, { J $ $ , known Variances unknown, large samples { { J , unknown $ $ {, $ {, Endpoints / / {J . { . / . / . / J { - { { { #{ - J . {J #{ { { % # - , # $ $ { { #{ , { $ #{ #{ #{ Hypotheses H" H# H" H# " Tests of Hypotheses Assumptions $ $ known 2 " Critical Region (Accept H#) 4 4 "- 4 4 {J . { " - {J . { 3. ". unknown $ " " known 3 $ unknown $ 3 . {J . { " . {J . { 4 " 4 $ 3 H" H# known " " $ . . unknown 4 Hypotheses $ H" $ " $ H# $ 2 " $ H" $ " $ $ H# " H" H# $ $ $ " $ " J 4 $ { J$ 3 % #{ J$ 3 { % { # # #{ #{ Critical Region (Accept H#) " 4 {J $ {J . { . { . { $ . { $ $ 4 $ {J # or J $ 4 { # #{ 4 $ # {J $ 3 $ # {J . { or 4 $ {J . { ...
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This note was uploaded on 05/18/2008 for the course MA 2222 taught by Professor Yang during the Fall '07 term at NYU Poly.

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