Let X be a continuous random variable with probability density function f(x). Determine the value of y for which E(|X - y|) is minimum.
Not sure where to even begin. Any help is appreciated.
I was always told this was the median and I think I got it.
I've never done this before, so here's my work...
NOW differentiate wrt y and use the fundamental theorem of calc...
Set that equal to zero produces F(y)=.5 meaning y is the median.