Appendix C Helpful Formulas

C.1 Positive and Negative Parts

For any number images , we define the positive part and negative part of x as, respectively:

equation

(Some authors use images .)

The following identities hold:

(C.1) equation
(C.2) equation
(C.3) equation
(C.4) equation

For any images , we have:

(C.5) equation
(C.6) equation

If images , then

(C.7)

C.2 Standard Normal Random Variables

Let with pdf f and cdf F. Let and be the ...

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