Probability and Statistics

Appendix C

Basic Results

C.1 Exponential Function e^x

e = 2.71828 18284 (Figure C.1)

e^x e^y = e^x+y

(e^x)^y = e^xy

Figure C.1 Exponential function e^x.

C.2 Logarithm

C.2.1 Natural Logarithm

ln x is the inverse of e^x and has base e (Figure C.2) and

e^ln x = x

ln(xy) = ln x + ln y

ln(x^a) = a ln x

Figure C.2 Natural logarithm (ln x).

C.2.2 Common ...