ECO220Y5 Lecture Notes - Lecture 4: Asthma, Cumulative Distribution Function, Random Variable
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Only difference between the 2 thoughts is the meaning they attach with probability. Random variables: discrete, variables that take on a set of discrete values, ex: roll a regular die. 6 possible outcomes: p. d. f = f(x) = p (x = x) (cid:1095) 1. P. d. f for a discrete random variable obeys 2 rules: (cid:4666)(cid:4667)=1: 0 (cid:1095) f(xi) (cid:1095) 1 (cid:3028)(cid:3039)(cid:3039) (cid:3043)(cid:3042)(cid:3029)(cid:3039) (cid:4666) (cid:4667, c. d. f = (cid:1832)(cid:4666)(cid:4667)= (cid:3028)(cid:3039)(cid:3039) (cid:4666)(cid:4667) (cid:1831)(cid:4666)(cid:4667)= (cid:3028)(cid:3039)(cid:3039) (cid:3043)(cid:3042)(cid:3029)(cid:3039) [ (cid:1831)(cid:4666)(cid:4667)](cid:2870)(cid:4666)(cid:4667: (cid:4666)(cid:4667)= (cid:3028)(cid:3039)(cid:3039) (cid:3043)(cid:3042)(cid:3029)(cid:3039, variable that has an infinite # of possible values, continuous. P. d. f for a continuous random variables obeys 3 rules: ex: unemployment rate, f(x) (cid:1096) 0. # on an interval; infinite: p. d. f = (cid:4666)(cid:4667) =(cid:4666)(cid:1853) (cid:1854)(cid:4667) (cid:3029)(cid:3028: (cid:4666)(cid:4667)=(cid:4666)(cid:1853) (cid:1854)(cid:4667) (cid:3029)(cid:3028, (cid:4666)(cid:4667)=1, c. d. f =f(x) = (cid:4666) (cid:4667) , (cid:1831)(cid:4666)(cid:4667)= (cid:4666)(cid:4667, (cid:4666)(cid:4667)= [ (cid:1831)(cid:4666)(cid:4667)](cid:2870)(cid:4666)(cid:4667) C. d. f = cumulative distribution function: probability that p(x (cid:1095) x, monotonically non-decreasing functions. They always either go up or stay the same as x increases; they never go down.
