 #1
 5
 0
Hello, I would like to differentiate the following expected value function with respect to parameter $$\beta$$: $$F(\xi_1,\xi_2) =\int_{(1\beta)c_q}^{bK+(1\beta)c_q}\int_{(1\beta)c_q}^{bK+(1\beta)c_q}\frac{\xi_1+\xi_22bK}{2(1\beta)^2} g(\xi_1,\xi_2)d\xi_1 d\xi_2$$ $$g(\xi_1,\xi_2)$$ is the joint pdf of the two random variables. $$b,K,c_q,\beta$$ are parameters in the problem. I tried using the hints given in a few other sites (http://math.stackexchange.com/quest...leintegralwithrespecttoupperlimits?rq=1) using Leibniz rule (and extending it to double integrals) but the correct answer eludes me. Additional information (if relevant): the statespace of the two random variables are as follows: $$\xi_1+\xi_2 \geq 2bK+2(1\beta)c_q, 2bK\leq\xi_1\xi_2\leq2bK. $$ I have uploaded the entire function from the paper I am referring to, and the regions defined by the random variables as a word document. Please let me know if you need more information. Appreciate any help.
Attachments

680.7 KB Views: 293