Transcription of Chapter 3 Continuous Random Variables
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Chapter 3 Continuous Random Variables
Chapter 3 Continuous Random IntroductionRather thansummingprobabilities related to discrete Random Variables , here forcontinuous Random Variables , thedensitycurve isintegratedto determine (Introduction)Patient s number of visits,X, and duration of visit, =value of function,F(3) = P(Y < 3) = 5/12x , pmf f(x)probability (distribution): cdf F(x)probability less than = sum of probabilityat specific valuesP(X < ) = P(X = 0) + P(X = 1)= + = (X = 2) = , pdf f(y) = y/6, 2 < y < 4probability less than 3 = area under curve,P(Y < 3) = 5/12xprobability at 3,P(Y = 3) = 0probability less than = value of functionF( ) = P(X < ) = : Comparing discrete and Continuous distributions7374 Chapter 3. Continuous Random Variables (LECTURE NOTES 5)1. Number of visits,Xis a (i)discrete(ii)continuousrandom variable,and duration of visit,Yis a (i)discrete(ii)continuousrandom (a)P(X= 2) = (i)0(ii) (iii) (iv) (b)P(X ) =P(X 1) =F(1) = + = (i)summation(ii)integrationand is a value of a(i)probability mass function(ii)cumulative distribution functionwhich is a (i)stepwise(ii)smooth increasingfunction(c)E(X) = (i) xf(x)(ii) xf(x)dx(d)V ar(X) = (i)E(X2) 2(ii)E(Y2) 2(e)M(t) = (i)E(etX)(ii)E(etY)(f) Examples of discrete densities (di)
Continuous Random Variables 3.1 Introduction Rather than summing probabilities related to discrete random variables, here for continuous random variables, the density curve is integrated to determine probability. ... is positive P(a < X < b) = F(b) - …
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