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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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