Monday, May 23, 2016

probability theory - Let X be a positive random variable with distribution function F. Show that E(X)=inti0nfty(1F(x))dx

Let X be a positive random variable with distribution function F. Show that E(X)=0(1F(x))dx



Attempt



0(1F(x))dx=0(1F(x)).1dx=x(1F(x))|0+0(dF(x)).x (integration by parts)




=0+E(X) where boundary term at is zero since F(x)1 as x



Is my proof correct?

No comments:

Post a Comment

analysis - Injection, making bijection

I have injection f:AB and I want to get bijection. Can I just resting codomain to f(A)? I know that every function i...