Financial Derivatives/Notions of Probability Theory

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Notions of Probability Theory[edit]

Here we introduce the notions of probability theory essential for the understanding of the book. The interested reader is referred to more thorough accounts of probability theory.

Useful distributions[edit]

Discrete distributions[edit]

For a thourough list of discrete distributions and their properties the interested reader is referred to Wikipedia on discrete distributions.

Binomial Distribution[edit]

The binomial distribution of parameters n \in \mathcal{N} and p \in [0,1]

P(X=k) = 	{n \choose k} p^k (1-p)^{n-k}

Poisson distribution[edit]

The poisson distribution with parameter \lambda>0, the intensity

P(X=k) =  \frac{\lambda^k}{k!} e^{-\lambda}

Continuous distributions[edit]