Basic Statistical Meth
Basic Statistical Meth ISYE 2028
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BIOL 20A - 01
Phuong 'Audrina' Hua
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This 0 page Class Notes was uploaded by Maryse Thiel on Monday November 2, 2015. The Class Notes belongs to ISYE 2028 at Georgia Institute of Technology - Main Campus taught by Kobi Abayomi in Fall. Since its upload, it has received 20 views. For similar materials see /class/234198/isye-2028-georgia-institute-of-technology-main-campus in Industrial Engineering at Georgia Institute of Technology - Main Campus.
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Date Created: 11/02/15
ISYE 2028 A and B Notation and Prerequisites Dr Kobi Abayomi January 8 2009 1 Introduction Just a brief review of some notation you should know and some short questions We often use roman letters XYy for things we hope to measure or model greek letters 04670 for quantities we7ll infer from directly measured quantities 2 Summation Notation We work with indexed vectors alot7 like or or any stuff stuf L7 stuffg7 stuff 2 mm stuff1 stuffz stuffn 1 1 1 is translated as Start with stuffl and add it to stuffg and keep on adding until stuff The stuff to do n times can be as simple to do as taking a bunch of numbers 1 2 and dividing it by the total number ie n n 2 1 z1z2xn i7 xi n n 71 11 11 or something more complicated like taking each of those numbers subtracting some other number squaring the result and dividing that by n 7 1 n 2 2293 i1 21 Product notation Just like summation but the indexed items are separated by multiplication in place of addition H951952 3 Integration differentiation exp log of simple functions should all be familiar from calculus Principally remember that inte gration and differentiation are linear operators meaning you can integrate and differentiate 7 usually 7 across sums 31 exp log You might have forgotten this important result about the derivative of the inverse of a function f f 1 The logarithm7 log7 function is de ned as the area under the curve 1t7 or logx idt 1 which implies that the derivative of the logarithm is l 10995 E With that remember that the exponential function is de ned as the inverse of the logarithm exp log l Then we have the very important result about the derivative of the exponent function expz 109 le 1 1 109 1 lore expo You remember that mp e the natural number in general expx em When I say 7 logx 7 I mean 7 loge 7 so that logem x You remember7 or can infer from the above7 that 109 10996 10m away cm In general aw 6110901 for any real number 17 with logam loge 9 zlogltagtl09lt6gt 10901 32 integrate differentiate We will look at multiple integration some time in the future Remember that you can usually switch the order of integration without too much trouble 7 cdf9ydydz b M d9ydyd jgltygtdy b fltzgtdz You should also remember the very important substitution method for integration7 with u 9W fudufudx And also integrate by parts lbwmlzing which might look more familiar to you if you let u f and 1 g 4 Suggested Exercises 1 210 Z39 7 when 0 is a constant 2 Ziori77when lrl lt1 3 H2 0 6 when x 17 z and c is a constant 4 If f a then f 7 if A is a constant 5 If g loganx then g z 7 if A is a constant