ch14estimationofmean,varianceandproportion

12 n2 nofthese ruleifyoureplaceaparameter

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Unformatted text preview: ... + X n 1 E( X ) = E( ) = {E ( X 1 ) + E ( X 2 ) + ..... + E ( X n )} n n 1 1 = {µ + µ + ........ + µ} = ⋅ nµ = µ n n X= i =1 i EXTRA INFO for Interest ∑X = xi − µ Z= σ ( xi − µ ) 2 Z2 = ~ χ 12 σ2 ( xi − µ ) 2 ∑ i =1 n n 2 ~ χn σ2 ( xi − x ) 2 ∑ i =1 σ 2 ~χ 2 n −1 Rule: If Z~N(0,1) is a standard Normal then Z² has a CHI­SQUARED distribution with 1 degree of freedom Rule: χ12 + χ12 + ....... + χ12 = χ n2 n of these Rule: If you replace a parameter by an estimate then you lose 1 degree of freedom. s2 = ( xi − x ) 2 ∑ i =1 n n −1 n 2 σ 2 χ n −1 ~ n −1 E ( s 2 ) = E{ i =1 2 2 n −1 ( xi − x ) 2 ∑ n −1 } σχ = E( ) n −1 σ2 2 = E ( χ n −1 ) n −1 σ2 = ⋅ (n − 1) n −1 =σ 2 Rule: The mean of a chi­squared distribution is equ...
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This note was uploaded on 02/22/2010 for the course FBE STAT0302 taught by Professor Unknown during the Spring '10 term at HKU.

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