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Session2

Session2 - Review of Probability and Statistics Dr Salman...

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1 Review of Probability and Statistics Dr. Salman Khan PhD. Finance

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2 Random Variables X is a random variable if it represents a random draw from some population a discrete random variable can take on only selected values a continuous random variable can take on any value in a real interval associated with each random variable is a probability distribution
3 Random Variables Examples the outcome of a coin toss a discrete random variable with P(Heads)=.5 and P(Tails)=.5 the height of a selected student a continuous random variable drawn from an approximately normal distribution

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4 Expected Value of X E(X) The expected value is really just a probability weighted average of X E(X) is the mean of the distribution of X, denoted by m x Let f(x i ) be the probability that X=x i , then n i i i X x f x X E 1 ) ( ) ( m
5 Variance of X Var(X) The variance of X is a measure of the dispersion of the distribution Var(X) is the expected value of the squared deviations from the mean, so 2 2 ) ( X X X E X Var m

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6 More on Variance The square root of Var(X) is the standard deviation of X Var(X) can alternatively be written in terms of a weighted sum of squared deviations, because i X i X x f x X E 2 2 m m
7 Covariance Cov(X,Y) Covariance between X and Y is a measure of the association between two random variables, X & Y If positive, then both move up or down together If negative, then if X is high, Y is low, vice versa Y X XY Y X E Y X Cov m m ) , (

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