stat400lec27 - Statistics 400 Lecture 27 Review Continuous...

Info iconThis preview shows pages 1–3. 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: Statistics 400 Lecture 27 Review Continuous distribution: Probability density function Properties of p.d.f f(x) : (a) f(x)>0; ( b ) ∫ = 1 ) ( dx x f ; ( c ) P(a<X<b) = ∫ b a dx x f ) ( Cumulative distribution function (c.d.f) F(x) = ∫ ∞- = ≤ x dt t f x X P ) ( ) ( F’(x)=f(x) Expected value of X or mean of X is ∫ ∞ ∞- = = dx x xf X E ) ( ] [ μ Variance ] ) [( ] [ 2 2 μ σ- = = X E X Var Standard deviation 2 ] [ σ σ = = X Var Moment-generating function M(t)=E[e tX ] Ping Ma Lecture 13 Fall 2005- 1 - Chi-square distribution with r degrees of freedom, ) ( 2 r χ E[X] = r r = 2 2 Var[X] = r r 2 2 2 2 = 100(1- ) α th percentile ) ( 2 r α χ 100 α th percentile ) ( 2 1 r α χ- Normal distribution ] 2 ) ( exp[ 2 1 ) ( 2 2 σ μ π σ-- = x x f ∞ < < ∞- x Let X be an observation from a distribution ~N ( μ , σ 2 ) To standardize a value of X: σ μ- = X Z Transform back to X If the random variable X is N ( μ , σ 2 ), then the random variable V=...
View Full Document

This note was uploaded on 07/24/2008 for the course STAT 400 taught by Professor Tba during the Fall '05 term at University of Illinois at Urbana–Champaign.

Page1 / 6

stat400lec27 - Statistics 400 Lecture 27 Review Continuous...

This preview shows document pages 1 - 3. Sign up to view the full document.

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