3.6 Class Notes - April 12 HWK #9 due R(4/19) or F(4/20)...

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April 12 HWK #9 due R(4/19) or F(4/20) 11.2: 8, 24, 27, 33 9.2: 4, 12, 16, 22, 27, 34, 40 Prelim 3 Tuesday April 24 7:30-9 in Uris Hall Auditorium Covers up to and including 9.2 Definitions 22 probability density expected A value mea () h a s () 0 and ( ) 1 The or The ( ) ( ) n va ( riance ) fx fxd x EX xf x dx xf x d x xfxd x µ σµ = == =− Uniform distribution with b=0 2 0 23 2 2 0 22 2 2 1 ( ) for [0, ] midpoint 33 341 2 b b a b b a x b b xxb EX dx bb xx b EX dx bbb EX =∈ = = = −=−= Uniform distribution formulas for the general case 2 2 2 1 f o r [,] 2( ) midpoint 2( ) 2 depends only on length 12 b b a a x ab ba EX dx ba ba σ −− −+ = Interpretations 2 The mean is the average value of The variance = ( ) ( ) measures how spread out the distribution is. The has the right units. For unifor st m ( ) /12 ( ) / 12 andard deviation X x d x σσ = Exponential 0 2 2 2 0 00 2 exponential ( ) mean 1/ , ' () 2, () 20 21 1 1 variance rt rt rt rt rt rt rt fx r e r EX t re dt ft t gt r e ft tgt e te te d t t re d t rr rrr r ∞∞ = + = + = =−= = ∫∫
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3.6 Class Notes - April 12 HWK #9 due R(4/19) or F(4/20)...

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