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.

Printable View

- Nov 16th 2010, 09:40 PMZennieMinimizing the expected value of a density function
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. - Nov 16th 2010, 11:28 PMmatheagle
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.