18.05 Lecture Notes - Lecture 5: Xu, Mit Opencourseware
Document Summary
1 learning goals: be able to nd the pdf and cdf of a random variable de ned in terms of a random variable with known pdf and cdf. If y = ax +b then the properties of expectation and variance tell us that e(y ) = ae(x)+b and var(y ) = a2var(x). Often, when looking at transforms of discrete random variables we work with tables. For continuous random variables transforming the pdf is just change of variables ( u substitution") from calculus. Transforming the cdf makes direct use of the de nition of the cdf. Let"s remind ourselves of the basics: the cdf of x is fx (x) = p (x x), the pdf of x is related to fx by fx (x) = f " Let x u (0, 2), so fx (x) = 1/2 and fx (x) = x/2 on [0,2].
