# stat400lec27 - Statistics 400 Lecture 27 Review Continuous...

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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=...
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## 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.

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stat400lec27 - Statistics 400 Lecture 27 Review Continuous...

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