APPENDIX BA COLLECTION OF USEFUL PROBABILITY DISTRIBUTIONS
B.1 UNIVARIATE DISTRIBUTIONS
- Gaussian distribution: X is a Gaussian random variable with mean μ and variance
if it has the following probability density function (pdf):
When X is such a Gaussian random variable, we denote it as
. Obviously in this case, 
and 
. - Standard Gaussian distribution: X is a standard Gaussian (or standard normal) random variable if
. The pdf of a standard Gaussian random variable X is
In other words,
and Var(X) = 1. - Lognormal distribution: X is a lognormal random variable with parameter μ and σ2 if it has the following pdf:
If X = eY where , then X is lognormal distributed.
- Exponential distribution ...
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