3.5 Class Notes

# 3.5 Class Notes - April 10 HWK#9 due R(4/19 or F(4/20 11.2...

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April 10 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 Why do we learn calculus? For example, probability densities are used in statistics. Calculus is needed to compute probabilities associated with them as well as their means and variances. Today and Thursday we will take a look at this topic which is covered in Chapter 11. Continuous probability distributions exponen Example tial di . The times between arrivals at the Burger King drive-up window have a stribution with rate n ( ) for 0 meaning that ( r ) i rt b rt i a T f t re t P a T b re dt = < < = Exponential continued 0 0 - (0 ) 1 (0 ) lim 1 1 Any probability density function has ( ) 0 and ( ) 1 The exponential has ( ) 0 for 0 b b rt rt rb i rb i b P T b re dt e e P T e f x f x dx f x x →∞ = = − = < ∞ = = = = < A less famous example 2 2 2 2 3 1 1 3 ( ) for 0 2 0 otherwise 8 3 8 1 7 (1 2) 8 8 8 8 ( 1) 0 so we can write or < x f x x x x P X dx

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