TA6 - ECO2121: Methods of Economic Statistics TA6 – 25...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ECO2121: Methods of Economic Statistics TA6 – 25 February 2009 “ A statistician is like an ice-cream chef. ” 1. Normal Distribution (a) Suppose X ~ Normal( μ , σ 2 ), then a X +b ~ Normal(a μ +b, a 2 σ 2 ). Hence, we get the “ standardization ” : Z = ( X – μ )/ σ ~ Normal(0, 1) (b) Suppose X ~ Normal( μ X , σ X 2 ) and Y ~ Normal( μ Y , σ Y 2 ) independently , then X ± Y ~ Normal( μ X ± μ Y , σ X 2 + σ Y 2 ). (c) This rule could be generalized as follows: The distribution of the linear combination of normally distributed random variables is Normal. Hence we need only the mean and the variance of the linear combination to characterize itself. By (revisited TA3 and TA5) E [ aX + bY ] = a E X + b E Y Var[ aX ± bY ] = a 2 Var[ X ] + b 2 Var[ Y ] if X and Y are independent We could know the target distribution. So following (b), what is the distribution of aX + bY ?...
View Full Document

Page1 / 2

TA6 - ECO2121: Methods of Economic Statistics TA6 – 25...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online