3.6 Class Notes

# 3.6 Class Notes - April 12 HWK#9 due R(4/19 or F(4/20 11.2...

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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 2 2 2 2 probability density expected A value mea ( ) has ( ) 0 and ( ) 1 The or ( ) The ( ) ( ) n va ( riance ) f x f x f x dx EX xf x dx x f x dx x f x dx µ σ µ µ = = = = = Uniform distribution with b=0 2 0 2 3 2 2 0 2 2 2 2 2 2 1 ( ) for [0, ] midpoint 2 2 3 3 3 4 12 b b a b b a f x x b b x x b EX dx b b x x b EX dx b b b b b EX σ µ = = = = = = = = = = Uniform distribution formulas for the general case 2 2 2 2 2 1 ( ) for [ , ] 2( ) midpoint 2( ) 2 ( ) depends only on length 12 b b a a f x x a b b a x x EX dx b a b a b a b a b a b a σ = = = + = = = Interpretations 2 2 2 2 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 f x dx b a b a µ σ µ σ σ σ σ = = = Exponential 2 2 0 2 2 2 0 0 0 2 2 2 2 exponential ( ) mean 1/ ( ) , '( ) ( ) 2 , ( ) 2 2 2 0 2 1 1 1 variance

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