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Mathematical Fundamentals

Mathematical Fundamentals. Properties of Logarithms: 1. Log b is strictly increasing If x<y then log b x < log b y Log b is one-to-one if log b x = log b y then x = y Log b 1 = 0 Log b b a = a (Log b b = 1). Properties of Logarithms: 2. Log b (xy) = Log b x + Log b y

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Mathematical Fundamentals

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  1. Mathematical Fundamentals

  2. Properties of Logarithms: 1 • Logb is strictly increasing • If x<y then logb x < 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 = x1p1+x2p2+ ... + xnpn • Usually written

  5. Summations

  6. Induction: Basis Step

  7. Induction: Inductive Step

  8. Integral Formulas a-1 a b b+1

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