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1. Random Variables and Probability Distributions - Professor ...

1. Random Variables and Probability Distributions - Professor ...

1. Random Variables and Probability Distributions - Professor

Business School, Brunel University MSc. EC5501/5509 Modelling Financial Decisions and Markets/Introduction to Quantitative Methods Prof. Menelaos Karanasos (Room SS269, Tel. 01895265284) Lecture Notes 1 1. Random Variables and Probability Distributions Consider a random experiment with a sample space : A function X, which assigns to each element ! 2 one and only one real number, is called a random variable. Example: We toss a coin twice. The sample space is and the probabilities of its events are = f(HH) ; (HT) ; (TH) ; (TT)g ; P (HH) = 1=4; P (HT) = 1=4; P (TH) = 1=4; P (TT) = 1=4: We now de…ne the function X-number of “heads”. In this case the outcome set, i.e. the space of the random variable X is Thus we can write S = f0; 1; 2g : P (X = 0) = 1 4 ; P (X = 1) = 2 4 ; P (X = 2) = 1 4 :

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