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Unformatted text preview: Revision material on probability Stock market prices are unpredictable and are modelled with random walks (or Brownian motion for continuous price models). The following material from Core A Probability will be assumed. Look in your course notes or a book if you need more detail. Higham is useful (but will not be followed closely) and relevant chapters will be indicated by H.x . H.3 Events and random variables: events are subsets of the sample space Ω and every event A ⊂ Ω has a probability P ( A ), where P obeys the standard axioms. A random variable X , say, is a mapping from Ω to R and we denote events by expressions like X ≥ 3, 1 < X < 5, ( X 1 = 3 , X 2 ≤ 4) which are abbreviations for { ω ∈ Ω : X ( ω ) ≥ 3 } etc. Random variables are called discrete when they map to a countable subset of R . The function p ( x ) = P ( X = x ) (defined for all real x ) is called the probability density function of X . The probability of any event described using X can be written as a sum e.g. P ( X ≤ 3) = ∑ x ≤ 3 p ( x ) so the density of X determines its probability distribution ....
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 Spring '10
 DrI.M.MacPhee
 Math, Normal Distribution, Probability, Probability theory, probability density function, Cov

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