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Sec3.1-3.2_427 - Chap 3 Discrete Random Variables...

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1 Chap. 3: Discrete Random Variables & Probability Distributions Random variable (RV) is a random object whose possible values are numerical . More formally (p. 87): RV is a function from S to the real numbers. Notation: RV’s: Capital letters X, Y, … Possible values: lower case x, y, …
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EX: Select a random stock S = {stock 1 , stock 2 , …., stock k } Prob. Model “equally likely”: so each stock has prob. 1 / k RV’s X = $ value. Possible values: {0, 1/8, 2/8,…} W = “cap” w = 1 for small cap w = 2 for large cap
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Discrete RV (Sect. 3.2) Discrete RV has possible values in a countable set: {x 1 , x 2 , x 3 , ….} (Continuous RV: Later) Prob. Distribution or Prob. Mass Function (pmf) of a discrete RV X is the function p(x) = P( X = x) for all real numbers x.
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Suppose k = 4 and W(stock 1 ) = 1, W(stock 2 ) = 1, W(stock 3 ) = 1, W(stock 4 ) = 2. Possible values of W: {1, 2} Prob’s : P(W=1) = P({stock 1 , stock 2 , stock 3 }) = .7 5 P(W=2) = .25
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Properties of pmf 1. p(x) = 0 for any x not in {x 1 , x 2 , ….} 2. p(x) > 0 for all x 3. S i p(x i ) = 1
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