Mathematics of Finance by Donald G. Saari

Author:Donald G. Saari
Language: eng
Format: epub
ISBN: 9783030254438
Publisher: Springer International Publishing

3.2.2 Random Variables

Recall that the expected value of a random variable X is

with the variance given by

(3.13)

where , the standard deviation, serves as a unit of “distance.”

To review the terms with a penny spinning on its edge, where the probability of getting a H is 0.3, if X(H) = 1, X(T) = 0, then X counts Heads:

and

Also recall that the standard form is

which, with the above numbers, is

Normal Distribution

For another example, let U ∼ N(0, 1), where N(0, 1) represents the PDF of the normal distribution with variance 1. The PDF is

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