MATH 226 - 10.8.2007

MATH 226 - 10.8.2007 - E(X – EX 2 Σ(x-EX 2 f(x o σ 2 =...

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MATH 226 – October 8, 2007 Random Variable o A real valued function of the sample space of the experiment o A real variable is discrete if the range consists of single points, and if it consists of an interval of real numbers then it is considered continuous Probability function o Assigns a real number f(x) to every value x of a discrete random variable X o ___ is constraint to f(x) ≥ 0 Σf(x) for all x =1 o We may think of probability as relative frequency P(X=x) = f(x) o Mean = X*f(x) Expected value o The expected value of the discrete random variable x is μ = EX = Σx*f(x) o The variance of a discrete random variable X is σ = Var(X)
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Unformatted text preview: E(X – EX) 2 Σ(x-EX) 2 f(x) o σ 2 = EX 2 – (EX) 2 = Σx 2 f(x) – (Σxf(x)) 2 book keeping function o cumulative probability function – probability of finding a value less than the one you want o F(x) = P(X≤x) o Σf(z) for z ≤ x Mathematically determined probability o Binomial probability o x ~ binomial (n,p) where n is the number of trials and p is the probability of success with one trial i.e. roll a die 5 times • x ~ binomial(5, 1/6) • P(x=4) = (1/6) 4 (5/6) 2 (6 choose 4)...
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