Probability Theory
- Random variables are usually written in upper case roman letters: X, Y, etc.
- Particular realizations of a random variable are written in corresponding lower case letters. For example x1, x2, …, xn could be a sample corresponding to the random variable X.
- or indicates the probability that events A and B both occur.
- or indicates the probability of either event A or event B occurring ("or" in this case means one or the other or both).
- σ-algebras are usually written with upper case calligraphic (e.g. for the set of sets on which we define the probability P)
- Probability density functions (pdfs) and probability mass functions are denoted by lower case letters, e.g. f(x).
- Cumulative distribution functions (cdfs) are denoted by upper case letters, e.g. F(x).
- In particular, the pdf of the standard normal distribution is denoted by φ(z), and its cdf by Φ(z).
- Some common operators:
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- E : expected value of X
- var : variance of X
- cov : covariance of X and Y
Read more about this topic: Notation In Probability And Statistics
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