Differentiation of Probabiity function

[Amol]

How to calculate d/dx of probability function Pr{v<= (x-K/1-c)} in equation

in order to maximize Z

Z=(K-x)*(Pr{v<=(x-K)/(1-c)}) + (cx-K)*(1-(Pr{v<=(x-K)/(1-c)}))

where K,c are constants

 

[Ishuda]

Assuming your probability function f(x) is defined on the interval (a, b), i.e.

Pr(x<a) = Pr(x>b) = 0,

then Pr{\(\displaystyle v \le \frac{x-K}{1-c}\)} is just the integral of f(x) from a to \(\displaystyle \frac{x-K}{1-c}\). Can you proceed from there?