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Piecewise Continuous Functions - Dartmouth College

math.dartmouth.edu

either. Intuitively, this makes sense, because it makes no sense to define a tangent line to a function at a point where it is discontinuous. We will learn a more mathematically-rigorous reason why a function has to be continuous at a point in order to have a derivative at that point in a couple of lectures. 3

  Make, Senses, Continuous, Piecewise, Piecewise continuous, Makes sense

A Conditional expectation - University of Arizona

www.math.arizona.edu

makes sense. We can think of it as a function of the random outcome !:! ! E[XjY = Y(!);Z = Z(!)] So it is a random variable. We denote it by E[XjY;Z]. In the continuous case we need to de ne E[XjY = y;Z = z] by a limiting process. The result is a function of y and z that we can once again interpret as a random variable. 3

  Make, Senses, Makes sense

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