Mathematical Fundamentals - PowerPoint PPT Presentation

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Mathematical Fundamentals

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Mathematical Fundamentals. Properties of Logarithms: 1. Logb is strictly increasing ... Logb ba = a (Logb b = 1) Properties of Logarithms: 2. Logb (xy) = Logb x ... – PowerPoint PPT presentation

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Title: Mathematical Fundamentals


1
Mathematical Fundamentals
2
Properties of Logarithms 1
  • Logb is strictly increasing
  • If xlty then logb x lt logb y
  • Logb is one-to-one
  • if logb x logb y then x y
  • Logb 1 0
  • Logb ba a (Logb b 1)

3
Properties of Logarithms 2
  • Logb (xy) Logb x Logb y
  • Logb xa a Logb x
  • xLogb y yLogb x
  • Loga x (Logb x)/(Logb a)

4
Probability
  • X(x1, x2, ... , xn) X is a set of numbers
  • P(p1, p2, ... , pn) P is a set of
    probabilities
  • For all 1 i n, pn is the probability of xn
  • Average x1p1x2p2 ... xnpn
  • Usually written

5
Summations
6
Induction Basis Step
7
Induction Inductive Step
8
Integral Formulas
a-1
a
b
b1
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