Help!!!!

[MillyMay]

the demand for a magazine is thought to be modelled by a Gamma distribution
with mean 10,000 and variance 1,000,000. A publisher prints and distributes 11,000 copies of this magazine each day. The profit on each magazine sold is $1, the loss on each magazine unsold is $0.25.

we know that the expectation E[.] of a function g(.) of a random variable X, having probability density function f(x) is given by E[g(X)]. For our magazine problem above, we know that f(x) follows a Gamma distribution. we need the function g(x) for net profit.

Can anyone help us to find this. Thanks

[MillyMay]

We've made an attempt to write g(x) in the form of F(x) as an integral but that doesnt work as the result is incredibly complicated and also if g(x)=x-(11000-x)/4, this doesnt work because x is the demand and if x is greater than 11000, the whole function should stop at 11000.

[Martingale]

the demand for a magazine is thought to be modelled by a Gamma distribution
with mean 10,000 and variance 1,000,000. A publisher prints and distributes 11,000 copies of this magazine each day. The profit on each magazine sold is $1, the loss on each magazine unsold is $0.25.

we know that the expectation E[.] of a function g(.) of a random variable X, having probability density function f(x) is given by E[g(X)]. For our magazine problem above, we know that f(x) follows a Gamma distribution. we need the function g(x) for net profit.

Can anyone help us to find this. Thanks


We've made an attempt to write g(x) in the form of F(x) as an integral but that doesnt work as the result is incredibly complicated and also if g(x)=x-(11000-x)/4, this doesnt work because x is the demand and if x is greater than 11000, the whole function should stop at 11000.

don't you just want

g(x)=1*x-11,000*.25

for x<=11,000

g(x)=0 otherwise