Is the following integral correct? (I wasn't certain what was meant by .)
Hi all,
I am new to the forum.
I have an integral that I am using, and I am unsure if I am computing the derivative of it correctly. I want to take the derivative of the following expression with respect to p:
int( p*[1-G(p-y)] + int(z*g(z)dz,-inf,p-y) dF(y) , -inf,inf)
where G is a CDF of z, and g is its pdf, and F is the CDF of y, -inf and inf are the bounds of the outer integral, and -inf and p-y are the bounds of the inner integral.
My calculation gives:
int( 1-G(p-y)-y*g(p-y) dF(y), -inf,inf ) where -inf and inf are the bounds of the integral.
Thanks for your help.
All the best,
Bob
I suspect I am committing a gross error, but isn't the derivative of a definite integral 0 because a definite integral is a constant the derivative of a constant is 0? If so, then isn't the answer to your question 0 because
is a definite integral?
Edit: I didn't notice the outside integral is with respect to y. I knew my solution was too easy! :P